Suppose that A tosses a coin which lands heads with probability pA, and B tosses one which lands heads with probability pB. They toss their coins simultaneously over and over again, in a competition to see who gets the 1st head. The one to get the 1st head is the winner, except that a draw results if they get their 1st heads together.

Calculate:

1. P(A wins);

2. P(B wins);

3. P(draw);

4. the distribution of the number of times A and B must.