Clue to Puzzle #57: Making a Fair Decision With a Biased Coin
My suggestion is that you think about what happens if you toss the coin twice. Work out the possible combinations of outcomes, and their probabilities.
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Let's have p be the probability of a Head, q be the probability of Tails, where obviously q = 1 - p. The table below shows the probabilities for the possible outcomes for the double toss.
|Head||HH pp||TH qp|
|Tail||HT pq||TT qq|
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