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 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.