OCR S1 2005 January — Question 6

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2005
SessionJanuary
TopicBinomial Distribution
TypeDirect binomial probability calculation

6 Louise and Marie play a series of tennis matches. It is given that, in any match, the probability that Louise wins the first two sets is \(\frac { 3 } { 8 }\).
  1. Find the probability that, in 5 randomly chosen matches, Louise wins the first two sets in exactly 2 of the matches. It is also given that Louise and Marie are equally likely to win the first set.
  2. Show that P (Louise wins the second set, given that she won the first set) \(= \frac { 3 } { 4 }\).
  3. The probability that Marie wins the first two sets is \(\frac { 1 } { 3 }\). Find P(Marie wins the second set, given that she won the first set).