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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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Looks good. (Did you notice that (1) already did half of the work for (3)?) – Brian M. Scott Dec 3 '12 at 21:34
Numbers are correct. – André Nicolas Dec 3 '12 at 21:38
I got the same answer for 1 and 3 but different for 2. I got 1/16. – Scorpio19891119 Dec 3 '12 at 21:45
Yep noticed that, but not in the exam hehe. – sonicboom Dec 3 '12 at 21:47
@Scorpio: You need the probability the sequence starts TTTH... given that the sequence starts T...... – Henry Dec 3 '12 at 22:18

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

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