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Probability of winning

Demetres on Friday, January 04 2013, 05:30 PM

Alice and Bob will play the following game: Alice will toss 2013 and Bob will toss 2012 fair coins. Alice wins if she gets more heads than Bob, otherwise Bob wins. What is the probability that Alice wins?

Demetres Christofides
    Replied by ZardoZ on Monday, January 07 2013, 05:10 PM · Hide · #1
    Supposing that Alice got 2012 heads and Bod 2012 heads (or equivalently Alice got 2012 tails and Bob 2012 tails), the solution to the problem lies in the result from the toss of the extra coin that Alice holds. So the probability that Alice wins is 1/2.
    • Demetres - more than a month ago
      Just to mention that even though the final answer is correct I am not convinced by the argument. As it stands there are more situations to consider.
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