Question: A box has three coins. One has two heads, one has two tails, and the other is a fair coin with one head and one tail. A coin is chosen at random, is flipped, and comes up heads.
a. What is the probability that the coin chosen is the two-headed coin?
b. What is the probability that if it is thrown another time it will come up heads?
c. Answer part (a) again, supposing that the coin is thrown a second time and comes up heads again.