two boys play basketball in the following way. they take turns shooting and stop when a basket is made. player a goes first and has probability p1 of making a basket on any throw. player b, who shoots second, has probability p2 of making a basket. the outcomes of the successive trials are assumed to be independent. i) find the probability function for the total number of attempts in the game. ii) on an average, for how long the game will continue? iii) what is the probability that player a wins?