Given an ‘unfair’ coin where , we can still use this coin to simulate a fair coin toss.

How?

In order to simulate a fair coin toss, we just need 2 events which are mutually exclusive and equally probable. Examining the probability of different outcomes when flipping our coin twice, we see that

and notice that . These 2 events are both equally likely and mutually exclusive, so they are exactly what we need to simulate a fair coin toss.

For example, our simulation could go as follows: We repeatedly flip the coin 2 times consecutively until we get a pair of results which are different, ignoring pairs which are the same. If the second result is a heads, we consider it to be as a heads from a fair coin toss, and likewise for tails.

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