A and B flip coins. A starts and continues flipping until a tail occurs, at which point

Question:

A and B flip coins. A starts and continues flipping until a tail occurs, at which point B starts flipping and continues until there is a tail. Then A takes over, and so on. Let P1 be the probability of the coin’s landing on heads when A flips and P2 when B flips. The winner of the game is the first one to get
(a) 2 heads in a row;
(b) A total of 2 heads;
(c) 3 heads in a row;
(d) A total of 3 heads.
In each case, find the probability that A wins.