You have a biased coin. You need to toss it to make a fair decision. Is there a way?
Ans: If you toss the coin twice. There are four possible outcomes: HH, HT, TH, and TT. Since the coin favours one side, the chance of HH will not equal the chance of TT. But HT and TH must be equally probable, no matter what the bias. So toss twice, after agreeing that HT means doing something and TH means doing the other. Should it come up HH or TT, ignore it and toss another two times. Repeat as necessary until you get HT or TH.
Ans: If you toss the coin twice. There are four possible outcomes: HH, HT, TH, and TT. Since the coin favours one side, the chance of HH will not equal the chance of TT. But HT and TH must be equally probable, no matter what the bias. So toss twice, after agreeing that HT means doing something and TH means doing the other. Should it come up HH or TT, ignore it and toss another two times. Repeat as necessary until you get HT or TH.
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