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Coins in a box: aa conditional probability problem

  1. Jun 27, 2013 #1
    I've been working on some questions from Rice's Mathematical Statistics and Data Analysis and I'm not sure about my solutions.

    The question I'm working on is as follows:
    1.8 #59c
    A box has 3 coins: 1 with two heads, 1 with 2 tails and 1 fair coin. A coin chosen randomly is flipped and comes up heads. If the coin is flipped again and comes up heads, what's the probability it's the two headed coin?

    My solution:
    Let A be the event the coin has two heads and let B be the event that heads is flipped twice.
    P(A|B) = P(A[itex]\cap[/itex]B) / P(B) = P(B|A)P(A) / P(B) = 1*(1/3) / P(B)

    P(B) = 1/3*1 + 1/3*1/4 = 5/12

    P(A|B) = 1/3 / 5/12 = 4/5

    Is this correct?
  2. jcsd
  3. Jun 27, 2013 #2


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    It looks right to me.
  4. Jun 28, 2013 #3

    Ps sorry mods, posted in wrong forum, please move to homework subforum.
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