A coin is flipped five times. For each of the events described below, express the event as a set in roster notation. Each outcome is written as a string of length 5 from {H, T}, such as HHHTH. Assuming the coin is a fair coin, give the probability of each event. (a) The first and last flips come up heads.
(b) There are at least two consecutive flips that come up heads.
(c) The first flip comes up tails and there are at least two consecutive flips that come up heads.