Saturday, November 14, 2009

Coin Toss

A boy tosses a fair coin repeatedly. Every time he gets a Head, he earns 1 penny, and every time he gets a Tail, he earns 2 pennies. He starts with no money. Prove that the probability of him at one time having exactly $n$ pennies is $\frac{2+(-\frac{1}{2})^n}{3}$

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