A coin that comes up heads with probability p is continually

flipped until the pattern H, H, T appears. (That is, you stop flipping

when the most recent flip lands tails and the two immediately preceding it lands heads.) Let X denote the number of flips made. Find

E[X]. You may leave your answer in terms of an equation in E[X]

and p. solution: Note that this problem is a modified version of one

of your homework problems. Proceed using one-step arguments.