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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. $\frac{5}{64}$
  • 4
    Looks good. (Did you notice that (1) already did half of the work for (3)?)2012-12-03
  • 0
    Numbers are correct.2012-12-03
  • 0
    I got the same answer for 1 and 3 but different for 2. I got 1/16.2012-12-03
  • 0
    Yep noticed that, but not in the exam hehe.2012-12-03
  • 0
    @Scorpio: You need the probability the sequence starts TTTH... given that the sequence starts T......2012-12-03
  • 0
    @Henry Yes, you are right. I did not notice that thing.2012-12-03

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