I'm not sure how to answer this question, and the assignment is due very soon. I don't need detailed explanations, just the basic working out.

2. [15 pts] You and I play the following game: I toss a coin repeatedly. The coin is not necessarily fair and P(H) = p ( the probability of getting a head is p) .The game ends the first time that two consecutive heads (HH) or two consecutive tails (TT) are observed. I win if (HH) is observed and you win if (TT) is observed. (a) [10 pts] Find the probability that I won the game. (b) [3 pts] Given that I won the game, find the probability that the first coin toss resulted in head. (c) [2 pts] If the game is fair, then p =