In Year 11 there are 80 students. Of these, 50 play a sport \((S), 25\) are involved in debating ( \(D\) ), and 20 do neither.
- Using this information, complete the Venn diagram. (2 marks)
- A Year 11 student is selected at random.
- What is the probability that the student plays a sport and is involved in debating? (1 mark)
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- Two Year 11 students are selected at random.
- What is the probability that both students are involved in debating only? (2 marks)
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Show Answers Only
a. \(\text{Venn diagram}\)
b. \(\dfrac{3}{16}\)
c. \(\dfrac{9}{632} \)
Show Worked Solution
a. \(\text{Venn diagram}\)
b. \(\text{Using the Venn diagram:}\)
\(P\text{(plays both)} = \dfrac{15}{80}=\dfrac{3}{16}\)
c. \(P\text{(both students involved in debating only)}\)
\(=\dfrac{10}{80} \times\ \dfrac{9}{79}=\dfrac{9}{632} (\approx 0.0142)\)