On each of three different occasions, a fair coin is flipped twice.
(a) On the first occasion, you witness the second flip, but not the first. You see that heads comes up. What is the probability that heads came up on both flips?
(b) On the second occasion, you are not present, but are shown a video of one of the flips, you know not which; either is as likely as the other. On the video, heads comes up. What is the probability that heads came up on both flips?
(c) On the third occasion, you are not present; a so-called friend teases you with the following information, that heads came up at least once in the two flips. What is the probability that heads came up on both flips?