Question: Suppose you are given a coin for which the probability of heads, say p , is unknown . How can you use this coin to

Suppose you are given a coin for which the probability of heads, say p, is unknown. How can you use this coin to generate unbiased, i.e., Pr[H] = Pr[T] = 1/2, coin flips? Give an algorithm for which the expected number of flips of the biased coin for extracting one unbiased coin flip is no more than 1/[p(1 p)].

1. Describe your algorithm in pseudocode. Comment your code.

2. Prove that your algorithm is correct.

3. Analyze your algorithm: what is the expected number of trials that your algorithm performs? Justify your answer.

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