Question

You roll a die twice and record the largest number (if the two rolls give the same outcome, this is the largest number). (a) Given that the first roll gives 1, what is the conditional probability that the largest number is 3? (b) Given that the first roll gives 3, what is the conditional probability that the largest number is 3?

Answer 1

To solve this problem, we can use the concept of conditional probability, which is the probability of an event occurring given that another event has already occurred.

(a) Given that the first roll gives 1, the conditional probability that the largest number is 3 is 0, because the largest number cannot be 3 if the first roll is 1.

(b) Given that the first roll gives 3, the conditional probability that the largest number is 3 is 1/6, because there is a 1 in 6 chance that the second roll will also give 3. If the second roll does not give 3, the largest number will still be 3 because the first roll gave 3.