CAIE S1 2014 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2014
SessionJune
TopicGeometric Distribution
TypeGame theory with alternating players

6 Tom and Ben play a game repeatedly. The probability that Tom wins any game is 0.3 . Each game is won by either Tom or Ben. Tom and Ben stop playing when one of them (to be called the champion) has won two games.
  1. Find the probability that Ben becomes the champion after playing exactly 2 games.
  2. Find the probability that Ben becomes the champion.
  3. Given that Tom becomes the champion, find the probability that he won the 2nd game.