The question is:

A fair die is rolled repeatedly. Let X be the number of rolls needed to obtain a 5 and Y the number of rolls needed to obtain a 6. Calculate E(X given Y=2).

So I thought since the number of rolls needed to obtain a 5 is independent from the number of rolls needed to obtain a 6. And since p=1/6 I thought maybe the answer is just 1/(1/6) which the expected value of a geometric distribution. But that's not correct.The actual answer is 6.6. Can someone please tell me what I am doing wrong?

A fair die is rolled repeatedly. Let X be the number of rolls needed to obtain a 5 and Y the number of rolls needed to obtain a 6. Calculate E(X given Y=2).

So I thought since the number of rolls needed to obtain a 5 is independent from the number of rolls needed to obtain a 6. And since p=1/6 I thought maybe the answer is just 1/(1/6) which the expected value of a geometric distribution. But that's not correct.The actual answer is 6.6. Can someone please tell me what I am doing wrong?

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