Question

Two boys play basketball in the following way. They take turns shooting and stop when a basket is made. Player A goes first with a probability p1 of making a basket on any throw. Player B, who shoots second, has probability 2 p of making a basket. The outcomes of the successive trials are assumed to be independent. (a) Find the probability mass function for the total number of attempts. (b) What is the probability that player A wins

Answer 1

P(A) = p1 (1 − q1q2)

Explanation:

Let A = player A wins,

then P(A) = p1 + (1 − p1)(1 − p2)P(A)

⇒ P(A) = p1 (1 − q1q2)