2022 TMJC P2 Q7
2022 TMJC P2 Q7
8 marks
Prelims
- A team of \(5\) people from a family of \(7\) adults and \(3\) children is to be selected for a competition. Find the number of teams that can be selected if
- there are no restrictions,[1]
- at most one child and the oldest adult must be in the team.[2]
- For events \(A\) and \(B\), it is given that \(\mathrm{P}\left( B \right)=\frac{17}{30}\), \(\mathrm{P}\left( A'\cap B' \right)=\frac{1}{3}\) and \(\mathrm{P}\left( \left. B \right|A \right)=\frac{4}{5}\).
- Find \(\mathrm{P}\left( A\cap B \right)\).[3]
- Find \(\mathrm{P}\left( A\left| \,B' \right. \right)\).[2]
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Answer:(a)(i) \(252\) (ii) \(75\) (b)(i) \(\dfrac25\) (ii) \(\dfrac3{13}\)
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