Consider an experiment in which a fair four-sided die (with faces labeled 0 , 1 , 2 , 3 ) is rolled once to determine how many times a six-sided die (with faces labeled 1 ,.., 6 ) is rolled. The die rolls are independent. Let X be the total number of times the six-sided die results in 5 or 6 .

Question

1. Calculate the conditional probability that X=2 given that the four-sided die roll resulted in 2.

2. Calculate P(X=2) .

3. Given that X=2 , what is the probability that the result of the four-sided die roll was 3?

Answer 1

1. The conditional probability that X=2 given that the four-sided die roll resulted in 2 is 1/3.

2. The probability that X=2 is 1/4.

3. Given that X=2 , the probability that the result of the four-sided die roll was 3 is 1/3.