77. A and B flip coins. A starts and continues flipping until a tail occurs. At this 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 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.