Two basketball players take turns trying to throw the ball through the hoop until one of the them succeeds. In detail, the first player throws the ball first: if the ball falls through the hoop, the game ends, but if not, it's the turn of the second player. Now if the second player makes the ball fall through the hoop, the game ends. If not, then the first player throws again, etc. During each throw, the first player succeeds with probability p1, while the second one with probability p2. Assume these probabilities satisfy 0 < P1 + P2. Let X1 be the number of throws made by player 1. Find the probability mass function of X1. Verify that it is a probability mass function.