Problem number two. Jessica rolls five dice. She rolls 19 points in total. What is the maximum number of sixes she could have rolled? Alright, so for this problem, we notice that she could roll two sixes and if she rolls two sixes, then the third die could be a five, the fourth die could be a one, and the fifth die could be a one. So we have 19 points. So we know that the answer is at least two. Now the question is, can we do three? If we can prove that we can't do three, but we can do two, then our answer would be two. So to show the maximum, we must show that three rolls of sixes are not possible. Well, if we have three rolls of sixes, what is the minimum point total that Jessica could have? Well, she rolls three sixes and then the other two dice, let's say they're the minimum, she rolls a one on both of them. That gives us a sum of 20, which is larger than the minimum or the larger than the sum of 19 that we want. And since that's the case, it's not possible for Jessica to roll three or more sixes and thus our answer would be C.

dice

maximum sixes

sum 19

probability

mathematics