Higher June 2019 Paper 5 Q18
18 21 people travelled to a meeting.
- 12 used a train.
- 6 used a car.
- 7 did not use a train or a car.
- Some used a train and a car.
Two people are chosen at random from those who used a train.
Find the probability that both these people also used a car. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{12}{132}\) oe | 6 | Accept dec or % equivalents (3 figures) 0.0909… or 9.09… % isw cancelling, conversion to other forms | |
| M5 for \(\frac{4}{12} \times \frac{3}{11}\) or B4 for \(\frac{4}{12}\) seen | Do not accept \(\frac{2}{6}\) alone For B4 accept \(\frac{1}{3}\) provided it does not come from \(\frac{2}{6}\) alone | ||
| or B3 for train [only] = 8, train and car = 4 or B2 for train and car = 4 or M1 for 12 + 6 + 7 – 21 oe | |||
| OR B2FT for correctly completed Venn diagram with \(12 - x\), \(x\) [their 4], \(6 - x\), 7 correctly placed FT their \(x\) (can be algebraic or \(x\) is an integer \(0 \lt x \leqslant 14\)) or B1FT for attempt at Venn diagram with \(12 - x\) or \(6 - x\) or 7 correctly placed FT their \(x\) (can be algebraic or \(x\) is an integer \(0 \lt x \leqslant 14\)) | For B2 and B1, condone no rectangle around Venn diagram | ||
| M1 for \(\dfrac{k}{n} \times \dfrac{k - 1}{n - 1}\) | where \(k \lt n\) and \(n \lt 21\) | ||
| If 0 scored, SC1 for \(\dfrac{k}{n} \times \dfrac{k}{n}\) soi | where \(k \lt n\) and \(n \lt 21\) | ||