Higher November 2024 Paper 4 Q15
15 In a survey, some students were asked whether they had travelled to school by bus (B) or by car (C) in the last week.
The Venn diagram shows some of the results.
(a) One of the students is chosen at random.
The probability that, in the last week, this student had travelled to school by bus and by car is \(\frac{1}{4}\).
The probability that, in the last week, this student had travelled to school by bus and by car is \(\frac{1}{4}\).
Find the value of \(n\). [3]
(b) One of the students is chosen at random.
Find the probability that, in the last week, this student had travelled to school by car given that they had also travelled to school by bus. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 24 | 3 | M1 for \(16 = \frac{1}{4}\) or 4 × 16 oe or 64 M1 for their 64 – 16 – 15 – 9 oe | Alt.: M1 for 16 × 3 and M1 for 48 – 15 – 9 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{16}{40}\) oe or \(\frac{16}{16 + \textit{their } 24}\) oe | 2FT | B1FT for \(\frac{16}{k}\) or \(\frac{k}{16 + \textit{their } 24}\) (both proper fractions) | FT their 24 |