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Jackie and Phil's Coins

Source: AIME 2010I Problem 4

March 17, 2010
probabilityfunctionnumber theoryrelatively primeAMCcoin flip

Problem Statement

Jackie and Phil have two fair coins and a third coin that comes up heads with probability 47 \frac47. Jackie flips the three coins, and then Phil flips the three coins. Let mn \frac{m}{n} be the probability that Jackie gets the same number of heads as Phil, where m m and n n are relatively prime positive integers. Find m \plus{} n.
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