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 flipped.
a) If the result of the flip is heads, what is the probability that the coin is two headed?
b) If the result of the flip is heads, what is the probability that a second flip of the same coin will also be heads?
c) If the selected coin is flipped twice and comes up heads twice in a row, what is the probability that the coin is two-headed?