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Problem 18

How many biased bits give an unbiased one?

Due: January 26
Points: 1

Supposed a coin is "biased" in that it gives heads with probability \(p\) and tails with probability \(1-p\), for some number \(0<p<1\). For example, if \(p=.75\), then the coin flip will come up heads (on average) three out of every four times.

Using the formula for Shannon entropy in the class notes, determine how many times this \(p\)-biased coin must be flipped in order to equal the entropy in a single unbiased coin flip.