OCR S1 2014 June — Question 7

Exam BoardOCR
ModuleS1 (Statistics 1)
Year2014
SessionJune
TopicPrinciple of Inclusion/Exclusion
TypeTwo-Way Table to Probability

7 The table shows the numbers of members of a swimming club in certain categories.
\cline { 2 - 3 } \multicolumn{1}{c|}{}MaleFemale
Adults7845
Children52\(n\)
It is given that \(\frac { 5 } { 8 }\) of the female members are children.
  1. Find the value of \(n\).
  2. Find the probability that a member chosen at random is either female or a child (or both). The table below shows the corresponding numbers for an athletics club.
    \cline { 2 - 3 } \multicolumn{1}{c|}{}MaleFemale
    Adults64
    Children510
  3. Two members of the athletics club are chosen at random for a photograph.
    (a) Find the probability that one of these members is a female child and the other is an adult male.
    (b) Find the probability that exactly one of these members is female and exactly one is a child.