A box has three coins in it. One has heads on both sides, one has tails on both sides, and the third is a fair coin with heads on one side and tails on the other. A coin is selected at random and °ipped.
(a) If the result of the °ip is heads, what is the probability that the coin is two-headed?
(b) If the result of the °ip is heads, what is the probability that a second °ip will also be
heads.
(c) If the selected coin is °ipped twice and comes up heads twice in a row, what is the
probability that the coin is two-headed?