In sports such as squash, played using English scoring, a player can score a point only when serving. If the serving player loses that rally, there is no score, and the serve goes to the other player. Suppose that the probability that Player A wins any rally is x, where 0 < x < 1, and that the outcomes of all rallies are independent.

(a) Explain why 

ƒ(x) = P(A wins the next point when B is serving)

       = x² + x(1 - x)^x2 + x(1 - x)x(1 - x)^x2 + ....

(b) Show that the probability in part (a) simplifies to(c) Show that

Transcribed Image Text:

f(x) x² 1 − x + x² * -