Welcome, Mr. Bagheer. I think we can get started now, so I'm going to try. Excellent. Hey, so first of all, just we wanted to start off by introducing ourselves. Well, that's on the next slide, but so let's start off by congratulating all of you. Congratulations to all the 2023 Math Kangaroo winners. Nice job. And all of your dedication and hard work is taking you this far. So we're trying to reward you by having a fun little math lecture today on probability and statistics. So I'm Bagheer. I have finished my bachelor's and master's in electrical engineering and computer science last year at Stanford, all in four years. I'm the co-founder of MetaPlus, and I've interned at large companies like Amazon and Microsoft in the past. And right now I'm a software engineer at a Silicon Valley startup. Just like many of you, I've been participating in Math Kangaroo for many years, and I placed first place internationally twice and was top 10 nationally many times. Hi, everyone. I'm Ms. Haripriya. I did my bachelor's and master's in electrical engineering and computer science in four years at MIT. So for those of you who guessed MIT, you were correct. This is a background of MIT. I'm also co-founder of MetaPlus, where we teach computational camps to students. I currently work as a software engineer at Microsoft, and I placed top 10 nationally in Math Kangaroo, as many of you as well. So as you probably saw the theme of our lecture today, it's called The Mysterious Disappearance of the Macduffin Macaroons, a lesson in paradoxes and fallacies and probability and statistics. So what is probability and statistics? I'm sure many of you know, especially if you've gotten this far, but just to establish some definitions. Probability and statistics is often concerned with random events. What is an event? It's the set of outcomes of a random experiment, and you have different sorts of events. So you can have independent events where the result of the second event is not affected by the result of the first event. So, for example, if you roll a dice many times, you know, the second time you roll a dice doesn't really impact or is not influenced by what you got the first time you rolled that die. Dependent event. So if the result of a second event is affected by the result of a first event. So the probability I will go on a bike ride if it is raining is basically zero because I don't want to bike in the rain. So the probability of it raining definitely influences the probability of me going out for a bike ride. Mutually exclusive events. These are two events that cannot occur at the same time. I cannot be both going out for a bike ride and sleeping in bed. The probability of both of those happening at the same time are, of course, zero. I can only do one thing with my time at a given point in time. Then what are mathematical paradoxes? So paradoxes in general are just something with an unexpected conclusion. And in mathematics, it's a mathematical conclusion so unexpected that it's difficult to accept, even though every step of the reasoning is invalid. And so I'm hoping that throughout the course of this event, you guys will build an understanding of why some paradoxes actually do make sense. And what are mathematical fallacies? So this is just improper reasoning that leads to an unexpected result that is patently false or absurd. I am so sorry. I have to take this. Just give me a second. Hello? Oh, it's my good friend, Dr. Roo. Dr. Roo, I'm teaching a class right now. Okay, I'm sorry. He says he wants to share something about his story with all of you. Oh, no. Oh, wow. Okay, it looks like something incredibly bad has happened at a party he's gone to. So he's just going to tell us what happened, if that's fine with all of you. We're just going to take a momentary pause from the presentation. It's more than momentary. Looks like Dr. Roo has a fuzzy connection. I'm Dr. Rue, and I was invited to a party at a haunted house. All my friends were invited. Dr. Fisher the Kingfisher, Miss Paws, Nostradamus the No-Fork Terrier, Anthony the Fox, Mr. Whiskers, Florence Nightingale, and of course I, Dr. Rue, the greatest mathematician in the world. And we were all competing for the famed MacGuffin Macaroon. Anthony the Fox, Mr. Whiskers, and Florence Nightingale were all particularly exemplary players who had at least won one coin during the night. Anthony the Fox had been winning all his games. We were enjoying our game when suddenly the MacGuffin Macaroon, the legendary sweet we were competing for, disappeared from its screw-shut glass box. Someone in the room must have stolen it. But who? I need your help. Wow. Okay. That's upsetting. Would you guys mind if we took actually a huge break from the presentation? We're just going to maybe help Dr. Rue deal with his problems for a second. And I don't know, maybe put in the chat if that's fine with you all. Dr. Rue does just want to make sure that the people who are helping him are mathematical geniuses. So luckily we do have all the winners of Math Kangaroo with us today. That's good. And he just wants to make sure all the definitions actually that I was giving you earlier, if you understood all of those for probability and stuff like that. So everyone understand what a paradox is, right? It's like, you know, sometimes you'll hear like you need experience to get a job, and you need a job to get experience. It's this kind of circular loop. Or, you know, fallacies, you might see proofs where like you can prove two equals to one when you divide by zero. Because there's some kind of flaw in that proof. So like, he's apparently dealing with a lot more of those. So as long as everyone's on board, we're going to move on and see if we can help him. Okay, so Dr. Rue sent us these facts. And there seems to be no objection in the chat. So we're just going to go ahead and help him. Dr. Rue said he and his friends were present at a 100% party where they were playing card games. The individual with the highest number of games won received the McGuffin Macaroon. And then there's three great players. Anthony the Fox, Mr. Whiskers, and Florence Nightingale. Anthony the Fox has actually won all of his games that night. And the McGuffin Macaroon, though, has been stolen. So we're going to try to find out who it was that stole it. And so this is our cast, you know, Dr. Rue and his friends. We have Miss Paws, Dr. Fisher, the King Fisher, Florence, the Nightingale, Mr. Whiskers. Miss Paws and Mr. Whiskers are cats. Dr. Rue, of course, the kangaroo. Nostradamus, the dog, and Anthony the Fox. So, okay, quiz number one. Dr. Rue wants to test what we are doing. You know, it makes sense. And we want to make sure we understand probability. Can someone help us out with solving this quiz? In fact, all of you guys can answer. Just choose the poll. If you can't see the polling feature, maybe if some of you are connected to Zoom over, like, an internet browser, please let us know, and you can type in the answers in the chat, and then we'll count it. My sister will write down who's doing what. Basically, these quizzes are where we're calculating the score for a special prize at the end. So the question is, given a fair coin and four coin flips, which sequence of events is more likely to be an actual sequence of coin flips? or any of them? 15 more seconds. I'm still waiting on a couple more people. And if you are unable to access the poll for some reason, if you can let me know in the chat right now, so I know to tally your score, it looks like most people are able to access the poll, though. So I'll give you five seconds to let me know if you aren't able to, and then I'll show the answer. Okay. Looks like everyone can access the poll. Thank you. Okay. And I've been, sorry, I've been having some issues with speaker notes. So I just want to make sure no one can see my speaker notes. Right. Yeah, no. Okay. Okay, great. Thank you. Okay. Yeah, we are ready. Mr. Excellent. Wait, can you close this? Oh, the poll. Yeah. Yeah. Okay. Thank you. Yeah. So, well, it's E is any sequence of four coin flips is equally likely. I mean, we might assign special significance to certain patterns. So maybe like, it seems significant to us that like, oh, four heads in a row. You know, someone gets that sequence, but, Maybe that's when predisposed to believe that sequence is less likely, but that's not the truth. But it is true to say that, you know, a combination of two heads and two tails is more likely than four heads, just because there's more permutations of two heads and two tails that you can get. So yeah. Answer is E. So Dr. Rue is calling us again. As a fortune teller, Ad Nostradamus can roll my tea leaves to divine who's the culprit. You have been guessing who will win these games from the start. And I have not had one correct answer. If we were to approach this as a scientific experiment, it would suggest that you have no magical powers of prediction. I admit that I've been wrong a lot today, but this is exactly why I'm due for the correct answer. Okay. So probabilistically speaking, if Nostradamus's predictions have been wrong so far, what would he do for a correct answer? This is. Let us know in the chat. No. Okay. Timothy says no. Oh, a lot of people say no. Whoa. A lot of people are vociferous about saying no. Okay. Behind. So I'm sure. William, Melody, Brandon, so mil Hannah, Japan, Toby. Aurora. Okay. Everyone's saying no. Oh, David's saying no. Okay. So is everyone familiar with the gambler's fallacy? So this is a common fallacy that says the mistaken. Oh, sorry. Yeah. This is a gap fallacy that says I'm staking belief about a sequence of random events. Sorry. It's a belief. Referring to. It's, it's a fallacy referring to the mistaken belief about a sequence of random events. So it basically is talking about how there's an incorrect belief often that people have, that if a particular event occurs more frequently than normal in past, it's less likely to happen than in the future. So for example, like, you know, if, if I roll a. A coin, you know, if I flip a coin multiple times, you know, and I, it lands on heads every single time, you know, the night, the probability that it will land on heads the next time, isn't less just because I've already gotten a streak of heads. Right. It's still 50%. And also. Nostradamus is saying, he's like divining what's going on with these tea leaves. Tea leaves are a memory less system where they have no state. It's not like. They're going to remember. Okay. People were wrong before. So now I'm going to be right. Right. Like there's no such thing. And also just describing a random value to the output of a random process. Shouldn't really mean anything. So there's all these reasons why Nostradamus is definitely wrong. But that brings us to quiz two. If you roll six on a dice, 10 times in a row, what is the probability that you will roll six again on your next roll? Given a fair six sided dice. Is it a still one six B greater than one six C less than one six or D it's impossible to roll six, 10 times in a row, let alone 11. And for those who joined in later, remember that we are competing here for a prize, so make sure to get that answer in before the time is up. I'll give you guys 30 more seconds. I'm waiting on one more. I'm closing it in 3, 2, 1. Okay. It is still one sixth, as hopefully most of you guessed. You know, of course, just like I said earlier with the coin in the flip example, there's no reason why you know the probability will change all of a sudden. And just a fun fact, if people are familiar with the game of roulette, in Monte Carlo, during a game of roulette on August 18, 1913, the ball fell on black 26 times in a row. So basically there's like almost 50% chance the ball will fall on black, almost 50% chance the ball will fall on red. And so people like did not expect such a long streak of black. This is an event with a 1 in 66.6 million chance. And so gamblers lost millions of francs as they assumed the ball would just end up, you know, ending its long black streak and then have a long red streak at some point. But it didn't. So yeah, you can never assume that just because some sequence of events has happened in the past that that will influence a future event, because it doesn't. You can even also prove it with probability, because think about it with this perspective, instead of thinking like, what's the probability of having, like, I don't know, six, or what's the probability of having 11 sixes in a row? What you're really asking is what's the probability of having 11 sixes in a row, given that you've already rolled 10 sixes? And so then it's just basically what's the probability that you'll roll a six on your next row, which is always one sixth. And so let's see, we are back. Well, earlier in the evening, when I was using today's horoscope to make predictions on the game winners, I was. Well, earlier in the evening, when I was using today's horoscope to make predictions on the game winners, I was. Well, earlier in the evening, when I was using today's horoscope to make predictions on the game winners, I was able to predict Anthony won every single time. I can use the horoscope to make a prediction about the culprit, since it's accurate. Okay, so we have some sort of way that Nostradamus has predicted the winner correctly every single time in a row, yet some apparently different prediction method besides this tea leaves. So what do we think about Nostradamus' claim on accuracy in horoscopes? Is this horoscope going to predict things accurately 100% of the time? I mean, it's worked so far, right? He's been able to predict that Anthony is going to win every single game. Oh, okay. There's a lot of nos in the chat. No budding astrologists here. Correlation. Oh, sure, yeah, just dropping that. Correlation is not causation in the chat. Wow, I love it. Okay. So, yeah, I think, you know, it seems a lot of people are not believers in horoscopes. That's definitely maybe up to personal preference. But yeah, it's, of course, just something, some word someone has written on a piece of paper. And definitely, we'll see about the accuracy, that accuracy itself is probably not the best metric for classifying a predictive model as, you know, a good model or a bad model. Because, you know, in this case, right, anyone who would have predicted Anthony to win would have had 100% accuracy rating since Anthony won every single game. So it doesn't really matter the method you chose to, you know, pick Anthony as your winner of every single game. It's just that if you happen to have that prediction, then you would be right 100% of the time. So Anthony was a good player. That just means he would have won every time. This doesn't prove the validity of the horoscope as a prediction mechanism, right? For those of you basketball fans in the chat. I mean, it's like if I were to bet on Michael Jordan, the Bulls winning every time they went to the finals. I mean, that's a safe bet, right? It's just it's not really showing that I have any powers of prediction. So let's test your ability to figure out, you know, what statements are good prediction and what statements are valid predictions. And so we have four statements. One is I predicted that it would snow yesterday in Colorado Springs. Two is I predicted it would snow yesterday somewhere in the world. Three is I predicted the sun will rise in the east. Four, I predicted that I would finish my homework. So each prediction has a score next to it. Add up the scores of all predictions that are valid, which means that they should take some actual skill to forecast in advance. It's not something that I'm influencing or that, you know, not really is not really much of a prediction at all. And yeah, let us know what the final sum is. So answering the polls, is it A, 0 to 1, B, 2 to 3, C, 4 to 7, or D, 8 to 15? And I'm joining from a different computer because I'm having some issues with presenting on this one actually is, can you just give me a panelist access. Yes. And I'm still waiting on five-ish more people, so I'll give you 15 more seconds. Reansh, can you change your answer after the fact? I'm not entirely sure. Reansh, if you want to, you can message me the answer you did think and I will take that answer as opposed to whatever you submitted. Okay, cool. Thank you, Reansh. Yes, Timothy, I have you down for the correct answer that you think it is. And Brandon, I see you messaged me your answer. Is it because you don't have access to the poll or did you also submit your answer to the poll? Okay, you did both. Cool. Yes, William, I have your new answer down. Okay. I will now... Access to the poll as much as possible. Can you hear us, Mr. Bagheer? Yes, I think my screen is... Okay, I can see you guys now. Awesome. So I'll end the poll here and share the results. Yeah, and if you can submit the answer in the poll, it's fine to just use the poll, but only if you can use the chat or, again, if something happened like this time where you want to change your answer. Yeah, and please try as much as possible, get the correct answer in the poll because it will be easier for me to tally. But if you do send me the chat, I will honor that answer. Okay, great. So answer is A. Thank you. So why is it A? So let's see. Let's start from the bottom. So I predicted that I would finish my homework. Now, is that something that really takes masterful powers of prediction or is it just an event that you can influence the outcome of by actually just doing your homework? It's the second one, right? If you just decide, hey, I'm going to do my homework tonight and then you predict, oh, I'm going to finish my homework, I mean, that's not really much of a prediction. Then saying I predicted the sun will rise in the east. I mean, at least on the planet Earth, that's what happens every day, at least if you're not at the North Pole or South Pole. And then I predicted that it would snow yesterday somewhere in the world. Again, it's a big world out there. I'm sure it's going to snow somewhere. Now, A, I predicted that it would snow yesterday in Colorado Springs. I mean, that's what a meteorologist does, right? They're doing some sort of forecasting. It's literally in the name, right? They're forecasting. So definitely it takes some actual skill to forecast something like that in advance, not only predict the time, but predict the place. So basically the first statement is the only correct, the valid statement. And so the final answer is A. Okay. All right, next video. I can narrow down the culprit with my legendary skills of deduction. You can observe coconut flakes on the clothes of Miss Paws. Macaroons are made from coconuts. Ergo, given that the thief has eaten the macaroon, they should be expected to be dusted in coconuts. So we must expect Miss Paws to be the culprit. Interesting. I can narrow down the culprit. Do we agree with Dr. Fisher's claim that Miss Paws is the culprit since she is dusted in coconut flakes? Awesome. Answers in chat already. Some nos, some yeses. Ooh, ooh, some yeses. Looks like we have a bunch of Sherlock Holmes joining us today. Rayan, future defense lawyer in the chat, I like it. Ha ha ha, Brandon, I think that's just the word spots. Aurora, asking the right questions, thinking like a lawyer or a detective, I like it. It could be another reason for the cochlear implant, same thing. Japan. Or, sorry, Orya, Orya, right? Same thing. Aro. Oh, Aro, sorry, Aro. And then, Dovi, who's on Latin in the chat, I literally have that quote right up on my wall. False talk, argo propter hoc. Yes, yes, yes. Deductive reasoning is not always correct. It could just be a coincidence. So the thing is, you know, we want to be careful when we jump to conclusions, right? We don't want to just say that just because one thing happened that, therefore, the other thing must have been the cause of this. We have to check, hey, are there any other possible causes, right? What Dovi said is, like, basically, since event Y followed event X, event Y must have been caused by event X. And that's a common example of a fallacy, where basically you're saying that, like, there's some correlation, again, between the events. Oh, sorry, there's some correlation between the events in the sense that, you know, A was followed by B. But that doesn't mean that there's a causation. So, yeah. No, no, no. Someone might have been selling macaroons at the party. But let me just say this up front. No one was selling macaroons at the party. So let's see. Is Ms. Paz innocent? Well, in order to understand that, first, we should break into some conditional probability. For those of you who are familiar with Bayes, if you go deeper into probability, eventually he will be your bae. So conditional probability, the probability that event A will occur given event B. This is how we represent it. This is the notation. So P of A given B. And then there's something called Bayes' law, which allows you to calculate the probability of A given B, even if you don't know it, by saying it's equal to the probability of B given A times the probability of A, all divided by the probability of B. So this determines the conditional probability of the event. Now, for this whole macaroon issue, we have to determine the probability that Ms. Paz has eaten the macaroon given coconut flakes were found on her. The logic is kind of backwards here. We should really be thinking about this, that given that coconut flakes were found, what is the probability that the thief has eaten the macaroon? Definitely not 100% because there could be other reasons why the coconut flakes are on the person, right? In fact, Ms. Paz apparently was seen eating coconut muffins earlier. And thus we know that there's a lower likelihood that she's the culprit. In fact, we can, let me write this out for you guys. So thank you, Mr. Rupert, for writing this out. We have P of A given B. So this is the probability of being the thief, given that there's coconut flakes. This is the probability of having coconut flakes, given that you're the thief. So let's pretend the thief ate it. Let's say we knew that for sure, right? Then, yeah, there's probably 100% probability that they have coconut flakes on them, right, if they're a sloppy eater. Okay, so that term is 100%. But then we have to multiply it by the probability of A, right, which is the probability of Ms. Paz, in fact, being the thief. And then the probability, divide it all by the probability of B, which is the probability of having coconut flakes on you. Now, even though this term is 100%, right, it's equal to 1, the probability of A may be low, right? We may not really think that there's a likely chance that Ms. Paz was the culprit to begin with. In fact, there are 100 people at the party, so we can say that she has a 1% chance of being the thief, so 0.01. And then what's the probability of having coconut flakes on her, especially given that she was eating coconut muffins earlier? Well, that's pretty high, right? In fact, let's say it's 100% because, I mean, she definitely was eating some coconut-based product earlier. Thank you, yes, Mr. Rupert, for putting that in the chat. Yeah, so substituting what A and B are. So in this case, we see that, you know, we have basically 1 times 0.01, all divided by 1, so that's just 0.01. So the chance of her being the thief is still 1%, doesn't really change anything. Okay, so, and this is also something called the overgeneralization fallacy. So, like, you know, there's a mistaken belief that a statistics about a particular population is asserted to hold among members of a group for which the original population is not a representative sample. So, yes, while it's true that, you know, someone who is the thief would have coconut flakes on them, that doesn't mean that everyone who has coconut flakes on them has a 100% chance of being a thief. And since Ms. Falls was eating coconut muffins earlier in the party, we're not going to accuse her of being the culprit right now anymore. Okay, so let's move on to our next video. I had a test that is 99% effective at detecting if someone has recently eaten a raspberry jam. I administered it to all hundred party guests and wrote down each result on a piece of paper and folded the paper using a map fold. Only one person, Mr. Whiskers, tested positive. We have found our culprit. Interesting. So, let's go on to the next slide. So, do we agree with Dr. Fisher's claim that Mr. Whiskers is the culprit since he tested positive on a 99% accurate raspberry jam test? So, this is a test that's 99% accurate and he tested positive. So, Melody is saying yes. Elena, Williams, they say no. Timothy said, we expect that one person tested positive. Okay, that's an interesting statement. Aiyu said probably. Ming-Heng said no. No. No. Soam said... Well, just to be clear, I don't know, the test was done with raspberry jam or something. It's not just that he had raspberry jam on his collar or something. This is a test that's accurate 99% of the time. And it happens to be done with raspberry jam. Hannah said no. Riyansh said no because of its 99... Oh, I like where Riyansh is going there. Minghao said no. Arav said most likely. Elena said it could be like the 1%. It could be 1%, yes. Elena, again, this is our defense lawyers in the chat here. Toby doesn't make sense. Sorry, what doesn't make sense? Like, you don't agree with Dr. Fisher? The question doesn't make sense. Brandon says no. Somal says no. Arav says, are we sure the culprit ate the macaroon? I guess we're not, right? Churya said no. There are 100 people there. Brandon said no. Aiyu, what if Dr. Fisher did it? Hannah, because the test has a 1% probability to be wrong and there are 100 guests. We know that the macaroon is raspberry jam. Thank you. Sorry. Just to be clear, I guess what you were saying earlier doesn't make sense. There could be raspberry jam from other places. Let me put it this way. The test is specifically for the raspberry jam that the macaroon has. Let's say it that way. Then Vihan says 99% times 100. What does that mean exactly? Let's think about that for a second. Somal, could have eaten the jam from another snack. Could have eaten raspberry jam earlier. A lot of people are making the jam objection. Let me just say the jam may have come, yes, from other snacks. Let's say this test pertains specifically to the raspberry jam found in the macaroon. David, no, because they're 100% raspberry testing. Okay. The map could have been so complicated that Dr. Fisher mixed up the results. Timothy, I love it. Okay. I like this. 1% test positive. Let's see. Let's see what's going on here. What's a false positive? This is an outcome where the positive class is incorrectly predicted. Basically, think of it like you're convicting an innocent person. Oftentimes, tests are used to diagnose, does someone have a disease or not? For example, let's say COVID. If your neuron remembers doing all those nasal swabs, there's a chance of a false positive. Which means it's possible that the test says you have COVID when, in fact, you don't. Now, let me also talk about false negatives just for a second. Basically, it's the opposite, right? Sometimes, it'll tell you like, oh, you don't have COVID when, in fact, you do. It'll say you're not the culprit when, in fact, you are. The false positive paradox is a situation where there are more false positives than true positives. Let me try to illustrate this for us. I don't want to give away too much. Let me do this through a question. Let's take this quiz. Let's think about Bayes' Law. Why don't you guys try to answer this question? We have a test that's 98% accurate on 100 people. How many additional people would we have to successfully test to bring our accuracy up to 99% without any additional false positives or negatives? Feel free to grab a paper and pencil for this one. I'll give maybe a minute more. I'm waiting still on like half of the participants. 30 more seconds. I'm waiting on like five-ish people. Give your best guess. As you know, that if you guess randomly, you have a 25% chance of getting it correct. 10 more seconds. So I think you're assuming that everyone is innocent, in which case there's a 36% chance everyone gets marked as innocent. But that means there's a 64% chance, right, of a false positive. Story was planned 99%. Okay, I'm going to shut the poll in 3, 2, 1, 0. Okay, so let me write this out for us using our pen. Okay, so we have 98% accurate on 100 people. If we have 100 people, how many people would be testing accurately? 98. How many people would have incorrect results? Two, right? What we're asking is, basically, how do we bring this test up? How do we bring its accuracy up to 99%? Let's say we don't have any more additional false positives or negatives, so we don't have anything more in this category, so this number stays consistent. How many more, basically, accurate tests would we need in this category in order to bring the average up to 99%? Basically, that means that, okay, if our rate of being inaccurate is 1%, right, and we know that 1% comes from just these two tests being inaccurate, right, what should the denominator be for this answer to be 1% or for this to simplify to 1%? It should be 200, right? Basically, that means that we need to test then 100 new people and get them all accurate, test them all accurately, get the accurate results for all of them in order to bring our accuracy up to 99%. So the answer is D. Thank you. Yes, and let me go back for a second just so I can explain then why this makes sense or why this doesn't make sense, the whole Dr. Fishers and Mr. Whiskers thing. We're going to write this out. So there's 99 people that are accurately... Sorry, the 99% that are innocent, right, 99 people are innocent, 1% is the criminal. So innocent and criminal. Now, if we are 99% accurate, right, with our tests, that means that out of those 99 people, right, what is our expected number of people who will test, like, as innocent? As innocent? Well, it's 98.01. People who are, in fact, innocent will test as innocent, right? However, so this is people who are, in fact, innocent, and this is how they test. Now, the people, there is one person, right, about 1% who is innocent, will not test as innocent, right, because there's a 1% chance we have an error, and across 99 people, that means we might expect there to be... I don't know why this is not letting me write on this part of the screen. This is really weird. Can you guys, you can't see anything, right? Okay, sorry, let me try writing over here. Okay, so 98.01 and 0.99. Does it make sense where these numbers are coming from? So, like, there's 99 people with times the 99% accuracy rate, so this is how many people I successfully classify as innocent, or I would expect to classify as innocent, 99 times 0.99. And over here is 99 times 0.01. 0.01. Okay, so that means I would expect to, basically, incorrectly classify one person, about 1% of this party. Now, we know that there's also one culprit at this party, right? So, what's the probability that we'll classify that criminal correctly? It's 99% still, right? So, that means I would expect 0.99 people to test positive, oh, sorry, yeah, test positive for being a criminal, and then 0.01 to incorrectly test positive for being a criminal. Now, of course, you know, a person can be divided into, like, 99 hundredths of a person, 100 hundredths of a person, but basically, these are just our estimates for numbers. So, does that make sense? So, this is people who are, in fact, innocent and test as innocent. These are people who are, in fact, criminals who test as criminals. But these are people who are innocent who test as criminals, okay? So, that means if you tested as being a criminal, right, what does that mean? Are you innocent or are you guilty? I mean, there's a 50% chance you're innocent, right, that you're actually innocent because this is a false positive. And there's a 50% chance you're a criminal. And then the reason why this is, is just because there are so few positives in general that despite the accuracy rate of this test being so high, there ends up being as many false positives as there are true positives. Does that make sense? And yes, thank you. Yeah, the table, this is called a confusion matrix. It's called a confusion matrix because these can be confusing and people have different formats. No, no, no. Yeah, so hopefully this makes sense though. This is true positives. This is true negatives. And false positives. And then false negatives. Did this make sense to everyone what's going on here? I don't know if that means yes or no or... Or just you find the confusion matrix. Yes, yes. Okay, great. So it makes sense to everyone that just because Mr. Rister's test is positive doesn't actually mean that he's guilty. It means there's a 50% chance he's guilty. But there's a 50% chance that he's still innocent because this was a false positive. Okay, great. So time for another quiz. So Houdini the Hare says he has a magical die that will roll a six each time he rolls it. You have not inspected the die. He rolls a six 15 times in a row and he says he can roll another six. Do you believe him? So the answer choice is A, no, because he's due to roll another number. B, no, because there's no such thing as magic. C, yes, he may roll another six. We can assume it's more than a one in six chance. And D, yes, he may roll another six. We can assume with a one in six chance. I'll give you 30 more seconds. Mr. Bagheer, Brandon says this story was planned 99%. There's a 1% chance it wasn't, you know. There's a 1% chance I actually received a call on my phone. Five more seconds, five, four, three, I'm still waiting on five more people. He's saying that he definitely will roll another six. Just to answer Timothy's question in the chat, this can be possible or has to. Like he says he has to, he says he will, for sure. Like he's betting on himself basically to roll a six. Is the quiz done? I guess Timothy has one more comment. Okay, okay, sure, let's change the wording, he's saying he will roll another six. I would try to change the presentation, but I'm afraid I'll break it all down. Rehansh, which answer do you want to lock in? Okay, so with that, I will end our poll and share the results. The correct answer is C. So I think Aurora kind of gave this away a bit in the chat. So here's the thing, I never said that the dice was fair, or the die is fair. So what's our probability, what do we think, is the die going to be fair or not? We can weigh this ourselves, we can say that, hey, yeah, we think there's like a 99% chance the die will be fair. But whatever the probability is, right, when you consider how unlikely it is for a six to be rolled 15 times in a row, right, then you have to start wondering, okay, is it actually fair? So this is an example of where like the gambler's fallacy does not actually apply. Because yes, something like a die that we know for sure to be fair, like, yeah, there's no such, you know, reason to assume that it's due for something. But here, since we don't know anything about the die, and you know, Houdini is a magician, and he's definitely doing some sort of trickery, right in the background, then that means that we should start suspecting at this point, you know, is it fair, right? And so let's think about these numbers, right? So and first of all, let me just go through and say why, yeah, A is of course false, because gambler's fallacy, B, there is no such thing as magic, but it is certainly possible to create illusions with preparation deception, or in this case, way to die. And then C, yes, that's the answer. And then D, I think that's probably too naive of an assumption to make. At this point, it's rational to assume the die is not fair, meaning he has more than a one in six chance. And so we can use Bayes' rule to see this. So what's the probability of a die being fair, given that we have 15 sixes in a row? Let me put this in the chat. So if you apply Bayes' rule, that means it's the equivalent to the probability of having 15 sixes in a row, given that the die is fair, times the probability of being fair, divided by the probability of having 15 sixes in a row. Now, it's hard to actually determine the probability of having 15 sixes in a row, given that we don't know how unfair the die could be. But let's just make up some numbers. Let's say the die is 99% likely to be fair, but in 1% of the time, it's likely to roll a six twice as much than we would expect it to. Then we are waiting for our prior for the die being fair very highly. We assume that even if it's unfair, we only have a twice as high of a chance of rolling a six, not rolling a six six. OK, and so if we do the math for that, because the chance of rolling a six 15 times on a fair die is something really, really small, if we actually plug in these numbers into our overall calculation, we say, OK, like 99%, we expect the dice to be fair. The probability we expect to roll a six 15 times on a fair die is like almost zero. And then we divide that by the overall probability of rolling a six 15 times. So 99%, it's a weighted probability, right? So 99% of the time, we're going to assume that we rolled it on the fair die, 1% we assume we roll it on the weighted die, which gives us twice as high of a chance to roll that six. And so if we calculate that out, there's a 0.3% chance that the dice is fair. I mean, the chance that the dice is unfair is 99.7%. And so we can just keep, and this is like, we're being pretty generous to Houdini and assuming as much as possible that the dice was fair. We're just leaving like a 1% chance for doubt. But let's say, again, we still assume that the dice is 99% likely to be fair, but the 1% of the time it's unfair, it'll roll a six 50% of the time. Then the probability that the dice is unfair would be 99.93%. So you can see that just because of how unlikely it is to roll a six 15 times in a row, it's very likely to be a weighted die. Does that make sense to everyone? Yes, OK. So I will move on to the next slide. I examined the scene near the light switch for clues and found a strand of hair. You know what this means? The culprit has been eating spicy salsa. Look at the experiment I conducted with various animals eating different levels of salsa. As you can see, the animals that ate the most salsa also shed the most. The ones that ate the least shed the least. All we need to do is find out who was eating the most salsa at the party. And we have our list of suspects. OK, so can we use Dr. Fisher's salsa test to predict who was near the light switch? So there are a lot of hairs near the light switch. It seems based on this chart that the more an animal eats salsa, the more hair they shed. Oh, some people are saying no straight off the bat. OK, interesting. I'm just curious. Can anyone explain why? You know? Yeah. No, not the salsa near the light switch. The hair was near the light switch. And Dr. Fisher has come to the conclusion that, you know, if a person has eaten a lot of salsa, they will shed a lot of hair. Not sequitur. Toby, I love the Latin. A non sequitur, by the way, means for everyone else. It does not follow. So like it's, I don't know, sometimes you just follow something up with an unrelated statement from the law of converse. I think I think you're referring to like what we're talking about right now, like what's like Bayes' law, like the probability of A given B is not equal to probability of B given A. Please explain how this test was conducted. Aurora, you're a born statistician. I mean, that is exactly the right questions to be asking. You always try to, you know, question the experimental design, see why it's flawed. Correlation is in causation. Some people say the animals with the most salsa consumed don't actually have the most hair sheds. Decreasing their hair could be there for a different reason. Some animals might not like salsa, but will shed a lot. You know, I really, really love the answers in this chat. Yeah. Some animals don't have hair. Some animals might not. Yeah. Yeah. So and, you know, Timothy, that's an interesting observation you made. So let's go on to the next slide. So, OK, this is our graph again, right? We have capsaicin in salsa, right? And actually, if you research, it actually helps with hair growth. So that means hair loss should decrease. And animals that shed the most hair were also selected to eat the most salsa in this experiment. So as you can see, you know, dogs, rats, mice, these are animals that definitely will shed more hair. Those were also the animals that happened to be given the most salsa, whereas a snake, a dolphin, you know, these are animals that don't really have a lot of hair or whiskers or any sort of, you know, fur for sure. Right. These were selected to eat the least salsa. And so when we say that they didn't shed as much hair, I mean, that's not really, A, meaningful because they don't have a lot of hair to begin with. And then B, as I think Timothy pointed out, actually, if you look at what's going on in this graph, if you look at the three different classes of animals, if you look at like each individual rectangle that we've drawn out here, the more that the salsa that an animal has eaten in their given class, actually the less they've shed. So even while the overall there's an upward trend, if you look at the animals in the classes that they're in, which is, you know, they only have a little hair to shed in general, and or, you know, these animals shed hair somewhat, you know, and these animals shed a lot. If you look at what they generally do. Right. In fact, salsa seems to be reversing the trend for them in their class. Right. So now they're shedding even less for hair. These are animals are shedding even less for hair. Does that make sense to everyone? Some things in the chat. I think dolphins have some whiskers. So yeah, snakes. I mean, I guess they can shed their skin. They have like false hair. Some people would call it hair. That's why subjects exposed to salsa. Exactly. They weren't the same as different levels. And I mean, we were changing so many things about this experiment. Right. Not just the salsa, but the type of animal. And thus, you know, it's not really like now we have two independent variables. It's not really a great experiment. And yeah, salsa is up to individual day. We don't know how much salsa each person has eaten. I mean, let's say for the purpose of this experiment, they were each animal was supposed to eat exactly a certain amount of salsa. But yeah, so this isn't great. What's the correlation of this graph? So yeah, let me let me get to that one second. And then if they shed their skin, I mean, the skin shed off, though, in like fragments. So it looks like hair is what I think Dr. Fisher's hypothesis was. That is a lot of work. But yeah, we can let's say maybe this is a one person job. I don't know. Maybe it's not. But let's see. So what we just saw here, though, in this graph, which I think is really profound, is a Simpson's paradox. And I think Timothy pointed this out to us earlier. So this is a statistical phenomenon where an association between two variables in a population emerges, disappears or reverses when the population is divided into subpopulations. So even though we saw an overall trend of the amount of hair that was being shed going up as salsa went up, if you look within the classes of or the categories of these are animals that don't shed a lot or don't have a lot of hair, these are animals that shed somewhat or have a little bit of hair. These animals shed a lot or have a lot of hair. You can see that, in fact, within those categories, the trend reverses. And it's also very much relevant to the concept of a confounding variable. In fact, like anytime you see Simpson's paradox emerges because you have a confounding variable. So this is a variable, an extraneous variable that is correlated with the independent variable and causally related to the dependent variable. So basically, because we're changing two of these variables at once, one was not only the amount of salsa being eaten, but also the second was the animal, that animal is a confounding variable. And in fact, we're seeing that that's if you factor that into our experiment, we can see that, in fact, the relationship between the independent and dependent variable reverses. So does that make sense? Hopefully, this is kind of cool and kind of mind blowing. It was mind blowing to me the first time I saw this. And it still is that you have an overall trend where things are going up, but within categories, things are going down. Oh. If you are familiar with baseball, there's a famous Simpson paradox example of Derek Jeter and David Justice, where if you look at the batting averages for particular years, it seems like David Justice is a better player. But if you combine the batting averages, it shows that Derek Jeter is a better player. Yeah. And so the reason why in this one is just because of the way the bats were taken helps cause Derek Jeter's batting average in his better year to outweigh the batting average in his worse year. And so in the overall batting average calculation, he does better, even though each year he did individually worse than David Justice. So I'll just write those out for those of you who can download it. Sorry, I was trying to get this on the slide earlier, but having a lot of technical difficulty. So let me just write this out. OK, let's see. So are there any other fallacies present here in this question? I mean, I think there's definitely many fallacies you can think of with trying to use SALSA as a way to diagnose if someone is, in fact, a culprit. But I think there's one of these choices that is better than the others. 30 more seconds. I'm going to keep this moving along. Waiting on five-ish more people. What are errors with Bayesian reasoning? Yeah, so for example, saying that basically anytime you're not really taking Bayes' rule into account. Wait a minute. Have I been writing my, oh my god, I've been writing so many messages just to the host and panelists. I don't think they've been going out to everyone. I'm so sorry. OK, but basically, it's like probability of A given B is not equal to the probability of B given A. That is, if someone thinks that they're equal or treats them as equal, then they're following creative Bayesian reasoning. OK, I will close the poll in 3, 2, 1. Let me just type it in. OK, so the correct answer is A. Let me know if anyone wants a reviewer for the other ones. But basically, that's exactly what's happening here with what I said earlier, the probability of assuming that just because a person has eaten a lot of salsa that they will show a lot of hair does not mean that the probability of shedding a lot of hair given that they've eaten a lot of salsa is high. They could be shedding hair for a lot of other reasons. A lot of people said correlation is not causation earlier, and that's true. So let me just type these out. Oh, please tell me if it, you know, I'm spending some time typing something out and it looks like you don't see anything. Please let me know. Hopefully, everyone's been following along. Why isn't it C is a question we have in the chat. OK, overgeneralization. So I would say overgeneralization, I mean, like while you could say in some ways that it's applicable, overgeneralization is more that you're applying something that, you're taking something that applies to one population and trying to extend it to everyone. And so let's say this was, let's even pretend, you know, even if we grant Dr. Fisher that his experiment was valid and that all salsa, sorry, that anyone who eats salsa will shed more hair, that doesn't, you know, his hypothesis would still be incorrect. Does everyone agree? Does that make sense? Just because people would sell such a hair? I mean, he's testing among a variety of population, right? He's testing tons of animals. So I think it's not necessarily overgeneralized, but his experiment at the end of the day wasn't great to begin with. So yeah, but I mean, I would say that to some extent, maybe, yes, you could say overgeneralization, but I would say that A was a better answer. After examining the crime scene for clues, I found screws lying here alongside a gold coin. The thief must have used this gold coin to unscrew the box and then left it here. Well, I guess there's an equal chance that Anthony or Florence is the culprit. After all, both had at least one gold coin. Interesting. So do we agree with Dr. Fisher's claim that Anthony and Florence can be culprits with equal probability because he found a gold coin near the glass box? A lot of people are saying no. Some people are saying yes. No. Okay, some fights in the chat. Interesting. Let's move on. So let's say you have three boxes. So box A has two gold coins, box B with one gold coin and one silver coin, and box C has two silver coins. You pick a box at random and then pick a coin. I'm sorry, and then pick a coin out of it without looking inside the box. You see that you've picked a gold coin. What is the probability you picked box A, B, or C respectively? Is it half, half zero, one third, two thirds zero, two thirds, one thirds zero, or impossible to tell since you're an alchemist who can transmute silver into gold? I mean, yeah, they still do have their coins, so in theory, we can just check who's missing one, if we have a warrant, I guess. Yeah, I mean, we can't violate people's Fourth Amendment rights, right? I mean, no reasonable search or seizure without a warrant. No unreasonable search or seizure without a warrant. Waiting on half people, half of the people still. Let's wrap this up in like 15 more seconds, just because we want to make sure we have time for all the quiz questions. Five, four, three, two, one, and I'm ending the poll now. Okay, so the answer is, can you see it? The answer is C. And so, let's see, why is it C? Well, there's a 0% chance we picked box C, right? Just because it doesn't have any gold coins. Now, what's the probability of picking box B, given that we've picked a gold coin? Well, if we follow Bayes' law, as you can see in the chat, it's basically the probability of picking a gold coin, given that we've picked A, times the probability of A, divided by the probability of picking a gold coin. The probability of picking a gold coin, given that we've picked A is one, the probability of picking A is one third. And then if we divide that by the probability of picking a gold coin, well, one third of the time, we have 100% chance of picking a gold coin. That's what's A. And then one third of the time, when we pick B, we have a 50% chance of picking a gold coin. That's with, yeah, picking box B. So if we sum that up, add up all the probabilities and then divide, we will get two thirds is the probability for picking box A. And another way you can think about it is just, if we're twice as likely to have picked a gold coin out of A as compared to B, if we assume in this diagram we've randomly picked a gold coin, two thirds of the time that coin is in box A. Does that make sense? Are Anthony and Florence, yes, Anthony and Florence are the only people who got gold coins. Correct answer is C. Yes. And hopefully D is ridiculous, but yes, I had to include it in there. So this is actually known as Bertrand's box paradox. This is a very famous problem. So it's a box containing two gold coins, box containing two silver coins and box containing one gold coin and one silver coin. So it's exactly what we saw. And nice for all of you got it. So why is this weird? This isn't displaying properly. That's really weird. I'm sorry. Are you seeing this slide or no? I'm seeing the Bertrand box paradox. There's nothing else. Yeah. OK. After choosing a box in random and redrawing one coin in random, if that happens to be a gold coin, what is the probability that the next coin will also be a gold coin? So that's basically just it's two thirds, right? Not one half. So just different ways of phrasing the same problem and thinking about it. OK, now quiz number eight. So let's say you have three boxes. Box A has two gold coins, box B with one gold coin and one silver coin and box C has two silver coins. So you pick a box at random and I take a look at both coins inside. I tell you that you have picked a box with at least one gold coin in it. What is the probability you picked box A, B or C respectively? A is half, half, zero. B is one third, two thirds, zero. C is two thirds, one third, zero. And D is same as before. Yeah. And by the way, like I asked in the chat, if you heard of the Monty Hall problem, it's essentially the same sort of idea. I think it's with cars and goats instead of gold and silver coins. Okay, waiting on one more person. There's a person named Paul Erdős, who's known as one of the greatest mathematicians of the 20th century, a very prolific author. He wrote, I don't know, tons of math papers, so much so that basically, like, people measure how good of a mathematician they are by how many, like, degrees of connections they are away from Paul Erdős. Anyway, he really got tripped up by this problem and he really hated it and got angry by it because he could not understand it. So hopefully... But most of you did. Yeah, most of you did. So... Oh, that's amazing. Okay. So the answer is A. And the reason why, there's no way we pick box C, of course, right? The probability of picking box A, given that we have picked a gold coin, if you follow Bayes' law, it's half, right? Alternatively, you can recognize that we have an equivalent probability of picking either box that contains at least one gold coin. One out of two is... Wait a minute. This is not the money hopper. Is this? Sorry. No, no, no. The next one is a Montreal problem. Oh, you've picked me up. Sorry. Yeah. The next one is a Montreal problem. I was hyping everyone up and I was like, wait, this is me. Okay. Sorry. So basically, it's a different way of asking the same question. This is actually similar to a problem known as the boy or girl problem, if you guys want to search that up later. And it's basically a lot of paradox of that problem is just the confusing wording. But as you can see, this is worded pretty similarly to the problem beforehand. But there are different answers. It's half, half, zero. Basically because we're saying, okay, it wasn't probably a picked a box, which at least... I've taken a look at both coins and I told you, okay, there's at least one gold coin inside. So does it make sense to everyone why this is the case? Okay. I'm just going to move on because yeah, I realized I got a little ahead of myself here. Okay. So we have quiz number nine. We have a box with two silver coins and one gold coin. You randomly pick up a coin without looking at it. I don't know why I keep on running. What is the probability that the coin you're holding is silver? Okay. So that's one part of the question. Now I can say, now I say that I'll look inside the box and remove a silver coin. What is the probability that the coin remaining in the box is silver? Three, two, one. Okay. Can I say it? Yes. Yes. The answer is B. So, this is the Montiel problem. But just phrased a little differently. This is what happens when you try to copy and paste from multiple sources. I have my answer, explanation over here. Sorry. Sorry. Brandon, I'll consider your answer. So, let me write this out because the formatting gets lost. I formatted well, but it's a little confusing. So, let's say you start off with gold. And then I pick out, I remove one silver coin, right? So, now what's left? It's one silver coin. But that's just one scenario. The other scenarios are, you know, you start off with the silver coin. I remove the other silver coin. Then what's left? It's a gold coin. Or you pick this silver coin. I remove another silver coin. What's left? It's a gold coin. And so, one-third of the time, you've picked the gold coin correctly, right? But two-thirds of the time, you haven't. So, that means you should, it's probably more advantageous for you to switch. And also, it just means that the answer is, what's the probability the coin you're holding is silver? It's more likely that it's two-thirds, right? And then what's the probability the coin remaining in the box is silver? It's basically the exact opposite, right? One-third. One minus one-third. Because regardless of whether or not we remove the silver coin, the probability that you didn't pick a silver coin initially is still one-third. Does that make sense why these two numbers also add up to one? Hopefully, it should make sense because they're basically mutually independent events. Okay. Hopefully, this makes sense to everyone. And this is the Monty Hall problem. This is a problem that one of the greatest mathematicians of all time had issues with. So, I will keep going if no one has any questions. I don't see anything in the chat. Okay. So, the probability, let's see, for the macro. So, in this case, we have claw marks on the glass because the thief wasn't able to open the box. So, the thief seems to have randomly pulled the coin out of the pocket. Very similar to the framing of the Bertrand box paradox. You know, it's a randomly pulled the coin out of a box, but in this case, a pocket. But we know that Anthony had 100 times as many gold coins as Florence because we know Florence had only one gold coin. Anthony had 100. So, then that means the probability that Anthony is the culprit is 100 out of 101. The probability of Florence being the culprit is 1 out of 101. Does that make sense why? Because, like, given that it's a gold coin, Anthony was 100 times more likely to be that person with the gold coin. All of Florence's remaining coins, not gold. So, that means the chance, you know, given that it's a random coin and given that it's gold, it's very likely to be Anthony, the culprit. And so, yeah, Anthony is the culprit with 100 times more chance. So, this is our prediction for the most likely thief. He had 100 gold coins in his possession. And also, just if we do want to give Dr. Fisher a little credit, you know, or sorry, go back to what Dr. Fisher was saying. Let's not give him any credit. It was a bad probability. But he's an animal that sheds a lot but ate very little salsa. So, you know, since we saw that more salsa actually helps with protecting your hair, you know, to some extent, one could argue that since he didn't eat as much salsa, that may have caused him to shed more hair. Although, of course, again, this was a terrible experiment and we shouldn't be doing any of that correlation causation stuff. Wait, so Anthony is the culprit. Anthony's horoscope said he would exhibit great skill but also fall prey to temptation. The horoscope predicted that Anthony would win all those games and that he was the bad guy. Why did you say the horoscope did not work? Horoscopes are pretty generic and meaningless. While there is a tenuous link between what his horoscope said and the reality appeared to be, in reality, Anthony won all his games by cheating. See, he had a fake set of playing cards. Did you know he cheated? It would be impossible for anyone to win all those games of Go Fish in a Row. The game largely depends on luck, not skill. Wait, aren't you guilty of committing the Gambler's Fallacy? And did you suspect that Anthony was the culprit because he was a cheater? Interesting. So, is Dr. Roo guilty of committing the Gambler's Fallacy? That's question number one. And question number two, did he suspect Anthony the Fox because he's a cheater? Yeah, that's an important question. People are asking, why would Anthony steal it if he's going to win anyway? Ooh, is this a plot hole? That's a good question. Not that it's a plot, Brandon. I mean, come on. 99% chance it's a plot hole, 1% chance it wasn't pre-planned. This could all be random. No. That's really good. We're thinking like detectives asking about the motive, Toby Branch. But no one's answering these questions here. Okay, so is Dr. Roo guilty of committing the Gambler's Fallacy? I'm just going to say straight up, the answer is no. Thank you, Melody. It's not impossible for him to win all these games, but maybe it was a hyperbole. Okay, that was a bit of a hyperbole. You're right. Did he suspect Anthony the Fox because he's a cheater? I don't think you can make that kind of argument, right? That would be saying correlation is, you know, like causation, right? So the Gambler's Fallacy, let's just revisit that. It's making a future prediction based on previous predictions in a game of chance where games have no relations and the probability of winning N plus one games given that a person has won N games is the same as them winning one game. So just because this is not a game of chance, right? Just because this is a game of like complete, or sorry, this is a game of chance. And just because, you know, this is very unlikely to have happened. It seems that, you know, one could argue that there seems to be something, you know, officially going on, just like with that, the problem with the die, where we were, we said, who do you need the hair had a way to die. But Dr. Roo didn't, you know, just go and rely on the probabilities. He was counting cards and seeing like, okay, was there any cheating going on? And that's how he knew that Anthony was cheating. Yeah, I mean, it's basically like, it's not impossible, but it's like very, very close to zero that he would win all these hundred games in a row of go fish. And now the second part, the second question, just because a pair of variables change, it doesn't mean one is causing the other to change. Or just because, you know, one thing is true, it doesn't mean the other thing is true, right? Correlation is not causation. So just because, you know, Nostradamus' horoscope and Anthony's unethical behavior in the card game may have correlated with his actions, right? But that did not cause him stealing the macaroon. And similarly, like just, you know, being a cheater in the game doesn't mean that he would steal the macaroon. So this is our final quiz question. Which of the following are examples of us committing the logical fallacy of assuming correlation implies causation? So A is people with smartwatches tend to be healthier, so smartwatches are good for your health. B, mispaws are sad every day that it happens to rain, so our sadness causes the rain. C, LDL cholesterol is associated with lower mortality, therefore higher LDL cholesterol increases mortality. And D, I walk two miles on days when my car is not working, thus not driving leads me to walk more. And E is A through C, F is A through D. So which one of these are committing the logical fallacy of assuming correlation is causation or implies causation? We only have a few minutes left, so I will be giving everyone... Waiting on I wish more people well give you guys five four three two one okay okay so the answer is e yes and uh just as a quick explanation people with smartwatches tend to be healthier so smartwatches are good for your health that's correlation right implying causation miss pause is sad every day so your sadness causes the rain that's definitely you know that's crazy uh and in fact for for a it could just be that in fact people who are healthier like to have smartwatches uh because they like to take care of their health and so it's actually the other way around you know them them being healthy and maintaining their health is what causes them to get smart watches uh then for c allele cholesterol is associated with low mortality therefore high allele cholesterol increases mortality it's not true i mean like signed i mean there's there's a variety of factors right that could be causing high cholesterol allele cholesterol and increasing mortality um you know so it's a some factor some different factor altogether right so they could be correlated that doesn't mean ldl cholesterol is the cost of such a thing um and these i walk two miles more on days when my car is not working that's not driving leads me to walk more i mean that's a natural consequence right um not being able to drive will cause me to walk so it is e since d is incorrect uh so wrapping up our mystery maybe in reality he stole the macro not because he wanted it but because someone paid him to someone who was afraid of losing the competition tonight look anthony had an uneaten macaroon and the pile of cash folded using the map fold if anthony wanted to eat the macaroon he would have he just wanted to prevent the competition from taking place this pile of cash must be from whoever hired him this is your signature fold isn't it dr fisher i noticed all night that you were leading us away from the true culprit with your poor statistics now it makes sense why wow we've got a lot of students to solve the mystery today yep wow amazing nice job guys a lot of people paying attention happy in reality he stole the macro not because he wanted it okay so dr fisher and anthony have both been arrested for their pride in these for their part in these crimes yes it was dr fisher who's the big behind everything um you want to make the announcement yes so now very quickly um please make sure to write your name and your email what we're going to do after the presentation over is over we're going to tally your scores and um you will be invited if you're one of our winners to participate in our ai in visual arts um camp brandon that's a that's a really good point you know um i was talking to my uh friend who has some chat gpt and he just you know automatically pulled these slides together you know just as we're talking this is this is all dr brew and chat gpt maybe there's a one percent chance okay this is our cast of characters this is dr yeah this is the real dr rue um one of us uh won this in a math kangaroo competition you can see in the t-shirt it's 2008 that might be before you were born but yeah i'm waiting for five more people to answer the name question um and then we'll i'll ask the email one uh can we quickly put down our names three more people can i close the poll okay 17 oh okay well that's fine um the next question's for email so oh were you waiting for me no i'm not waiting for you i was waiting for the students a a couple of students i'm going to end this poll um you can put a name in the chat if you didn't get to it um i want to launch the email question uh by the way if you want to learn other cool topics you know miss pause and mr risk they're our brand ambassadors and um you can check out our youtube channel we also are on tiktok yes is there any more slides uh there's one more slide uh the quiz results i mean we'll release them yeah okay cool yeah that we will release after the slide so make sure to uh you can put multiple emails yeah um yeah i'm still waiting for like five more people on the email question um it does end at uh 11 30 so if you have put your name and email then you are all set and feel free to drop off if you have any questions feel free to you know stay on and chat but um yeah make sure to put your name and email um and it was great uh it was great teaching you all today yes and please let us know if you have any questions uh we will send them to miss smitheason and i think she will send them hopefully out in the next week or two yeah next week or two thank you all for being such a great audience

probability

statistics

Math Kangaroo

independent events

conditional probability

Bayesian reasoning

gambler's fallacy

correlation vs causation

interactive quizzes

statistical reasoning

critical thinking

mystery resolution