Most everyone has made a decision by flipping a coin. However, there is no such thing as a fair coin (one that has equal probability of being heads and tails). So how then are you suppose to make a fair decision when using a coin? After answering this puzzle you will know.
You have an unfair coin with the probability of being heads some unknown value, Prob(Heads) = p. And you know p is not equal to 0.5. How can you then generate a fair toss? [Answer after the break]
Since the coin has a Prob(Heads) = p, it has a Prob(Tails) = 1-p. If you toss the coin twice, you have four possible outcomes, HH, TT, HT, TH. Prob(HH) = p*p. Prob(TT) = (1-p)*(1-p). Prob(HT) = p*(1-p). Prob(TH) = (1-p)*p.
So you can see that if you flip the coin twice and treat a HT as one possible out come and TH as the other, you can make a fair decision. During the toss, if you get a HH or TT, you need to start over to remain fair. In other words, if you get a H or T followed by the same thing, you need to start the toss sequence over. Otherwise the outcome is predetermined.
Puzzle courtesy of Professor Siva.
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