I toss a coin repeatedly. The coin is unfair and P(H) = p. The game ends the

first time that two consecutive heads (HH) or two consecutive tails (T T) are observed. I

win if HH is observed and lose if T T is observed. For example if the outcome is HT HT T ,

I lose. On the other hand, if the outcome is T HT HT HH , I win. Find the probability that

I win.