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 .

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?

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