Grades 11-12 Video Solutions 2024-2024_11-12

Video Transcription

Kim has modified a regular 6-sided die so that the probabilities of rolling a 2, 3, 4, or 5 are still 1 6th each,  but the probability of rolling a 6 is twice the probability of rolling a 1. What is the probability of rolling a 6?  Let P1 be the probability that we roll a 1 and P6 be the probability that we roll a 6.  Then, we know that the probability of rolling a 1 or 6 is just the sum of these, which is equal to 1 3rd. We also know that P6 is twice P1, and thus P1 is half of P6.  Solving this equation, we can find that P6 is 2 9ths.

Video Summary

Kim has modified a 6-sided die such that rolling a 2, 3, 4, or 5 each has a probability of \( \frac{1}{6} \). The probability for rolling a 6 (\( P6 \)) is twice that of rolling a 1 (\( P1 \)). Given that \( P1 + P6 = \frac{1}{3} \) and \( P6 = 2 \times P1 \), these equations are solved to find that \( P6 = \frac{2}{9} \).