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You play a game where you first choose a positive integer n and then flip a...

You play a game where you first choose a positive integer n and then flip a fair coin n times. You win a prize if you get exactly 2 heads. How should you choose n to maximize your chance of winning? What is the chance of winning with optimal choice n? There are two equally good choices for the best n. Find both.

Hint: Let fn be the probability that you get exactly two heads out of n coin flips. Derive conditions when fn < fn+1 and fn > fn+1.

Math   Statistics-And-Probability   
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