This problem requires careful attention to the sequence of events.

If you flip a coin 3 times, the probability of getting the sequence HTH is identical to the probability of getting HTT (1/8). Lets make this situation a little more interesting. Suppose you are going to flip a coin until you get the sequence HTH. Say this takes you x flips. Then, suppose you are going to flip the coin until you get the sequence HTT. Say this takes you z flips. On average, how will x compare to z? Will it be bigger, smaller, or equal? Explain why.