In this problem we will derive fair coin flips from biased coins: that is, given coins for which…
In this problem we will derive fair coin flips from biased coins: that is, given coins for which the probabilities of landing heads and tails are not equal, the problem is to construct an experiment for which there are two disjoint events, with equal probabilities, that we can call “heads” and “tails.”
(a) Given c1 and c2, where c1 lands heads up with probability and c2 lands heads up with probability 1 4 , construct a “fair coin flip” experiment.
(b) Given just one coin, with unknown probability p of landing heads up, where 0
(c) In your solution to part (b), what is the chance that a single trial of your experiment results in an outcome of either heads or tails?