Bonny and Sally are playing in a tennis tournament. On average, Bonny makes 80% of her shots,

Question:

Bonny and Sally are playing in a tennis tournament. On average, Bonny makes 80% of her shots, whereas Sally makes 75% of hers. Bonny serves first. At right are tree diagrams depicting possible sequences of events for one and two volleys of the ball. (A volley is a single sequence of Bonny hitting the ball and Sally returning it.) Once a ball is missed, that branch ends.

a. What is the probability that Bonny will win the point after just one volley?
b. What is the probability that Bonny will win the point in exactly two volleys?
c. Make a tree diagram to represent three volleys. What is the probability that Bonny will win the point in exactly three volleys?
d. What is the probability that Bonny will win the point in at most three volleys?
e. What kind of sequence do the answers to 9a-c form? Explain.
f. What is the probability that Bonny will win the point in at most six volleys?
g. In the long run, what is the probability that Bonny will win the point?