Consider the following scenarios, where we apply probability to a game of flipping coins. In the game, we flip one coin each round. The game will not stop until two consecutive heads appear. (a) What is the probability that the game ends by flipping exactly five coins?

(b) Given that the game ends after flipping the fifth coin, what is the probability that three heads appear in the sequence?

(c) If we change the rule that the game will not stop until three consecutive tails or three consecutive heads appear, what is the probability that the game stops by flipping at most six coins?