June 2024 Paper 2 Q5
5 \(M\) is the event that an A-level student selected at random studies mathematics.
\(C\) is the event that an A-level student selected at random studies chemistry.
You are given that \(\mathrm{P}(M) = 0.42\), \(\mathrm{P}(C) = 0.36\) and \(\mathrm{P}(M \text{ and } C) = 0.24\). These probabilities are shown in the two-way table below.
| \(M\) | \(M^{\prime}\) | Total | |
|---|---|---|---|
| \(C\) | 0.24 | 0.36 | |
| \(C^{\prime}\) | |||
| Total | 0.42 | 1 |
(a) In the Printed Answer Booklet, complete the copy of the two-way table. [2]
(b) Calculate the probability that an A-level student selected at random does not study chemistry given that they do not study mathematics. [2]
| Scheme | Marks | AO | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B1 B1 | 1.1 1.1 | ||||||||||||||||
| [2] |
Notes
B1: entries in bold
B1: 0.46
| Scheme | Marks | AO |
|---|---|---|
| \(\frac{\textit{their}\ 0.46}{\textit{their}\ 0.58}\) oe | M1 | 1.1 |
| \(\frac{23}{29}\) or 0.79(31..) | A1FT | 1.1 |
| [2] |
Notes
M1: must use values from their table; \(0 \lt\) their \(0.46 \lt\) their \(0.58 \lt 1\)