Many everyday decisions, like who will drive to lunch or who will pay for the co

Question

Many everyday decisions, like who will drive to lunch or who will pay for the coffee, are made by the toss of a (presumably fair) coin and using the criterion "heads, you will; tails, I will." This criterion is not quite fair, however, if the coin is biased (perhaps due to slightly irregular construction or wear). John von Neumann suggested a way to make perfectly fair decisions, even with a possibly biased coin. If a coin, biased so that P(h) equals = 0.4900 0.4900 and P(t) equals = 0.5100 0.5100, is tossed twice, find the probability P( hh hh).

Explanation / Answer

P(h) = 0.49, P(t) = 0.51

If the coin is tossed twice, the probability of two consecutive heads, P(HH) = 0.49 x 0.49 = 0.2401

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