A survey of 50 students found that:
- 28 students study Mathematics (set \(M\))
- 22 students study Physics (set \(P\) )
- 12 students study both Mathematics and Physics.
- How many students study Mathematics or Physics, or both? (1 mark)
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- If two students are chosen at random, what is the probability that both DO NOT study either Mathematics or Physics? (2 marks)
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Show Answers Only
a.
\(n(M \cup P)=38 \ \text {students}\)
b. \(\dfrac{66}{1225}\)
Show Worked Solution
a.
\(n(M \cup P)=38 \ \text {students}\)
b. \(P(M \cup P)=\dfrac{38}{50}\)
\(\text{Student 1:}\ P(\overline{M \cup P})=1-\dfrac{38}{50}=\dfrac{12}{50}\)
\(\text{Student 2:} \ P(\overline{M \cup P})=\dfrac{11}{49}\)
\(\therefore P\left(\text{Both study neither }\right)=\dfrac{12}{50} \times \dfrac{11}{49}=\dfrac{66}{1225}\)