Answer to Question #32802 in Math for Riaan

Question

In the game of tennis a player has two serves. In the first serve is successful the game continues. If the first serve is not successful the player serves again. If the second service is successful the game continues. If both serves are unsuccessful the player has served a ‘double fault’ and loses the point.
Gabriella plays tennis. She is successful with 60% of her first serves and 95% of her second serves.
Draw a tree diagram

Answer 1

Тhe probability that Gabriella serves a double fault = (1-0.60)(1-0.95) = 0.02
Тhe probability that Gabriella wins the point = 0.75 + (1-0.75)(0.5) = 0.875