Chapter 11.3, Problem 87E

Fair Decisions from Biased Coins 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

$P(\text{h)=0}\text{.5200})\text{and}\text{P(t)=0}\text{.4800}$

is tossed twice, find each probability. Give answers to four decimal places.

Having completed Exercises 83-86, can you suggest what von Neumann’s scheme may have been?