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I had an exam today and I would like to know for sure that I got these answers correct.

A fair coin will be tossed repeatedly.

  1. What is the probability that in 5 flips we will obtain exactly 4 heads.
  2. Let $X =$ # flips until we have obtained the first head. Find the conditional probability of $P(X=4|X\geq2)$.
  3. What is the probability that the fifth heads will occur on the sixth flip?

Here are my answers:

  1. $\frac{5}{32}$
  2. $\frac{1}{8}$
  3. $\frac{5}{64}$
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    @Henry Yes, you are right. I did not notice that thing.2012-12-03

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It seems that the general consensus is that you are right.