Interview Question: Two Heads Better Than One?

Sample Question #65 (probability puzzle)

I have 100 coins, with all but one of them normal. The last one has two heads. I put these coins into an opaque jar and shake the closed jar. I ask you to pick out a coin from the jar, and you observe a head on the coin you just took out. What is the probability that this coin is the double-headed coin?

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One Response to Interview Question: Two Heads Better Than One?

  1. Brett says:

    ANSWER
     
    This question can be easily solved using Bayes’s Rule, which is
     
         P(A|B) = P(B|A)P(A) / P(B)
     
     So, let A=getting the double-headed coin and B=seeing a head, we get
     
         P(A|B) = (1)(1/100) / (101/200) = 2/101.
     

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