CAIE S1 2018 June — Question 3

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2018
SessionJune
TopicTree Diagrams
TypeFind unknown probability parameter

3 The members of a swimming club are classified either as 'Advanced swimmers' or 'Beginners'. The proportion of members who are male is \(x\), and the proportion of males who are Beginners is 0.7 . The proportion of females who are Advanced swimmers is 0.55 . This information is shown in the tree diagram.
\includegraphics[max width=\textwidth, alt={}, center]{dd75fa20-fead-48d6-aff4-c5e733769f9f-04_435_974_482_587} For a randomly chosen member, the probability of being an Advanced swimmer is the same as the probability of being a Beginner.
  1. Find \(x\).
  2. Given that a randomly chosen member is an Advanced swimmer, find the probability that the member is male.