Higher November 2019 Paper 5 Q16
16 50 people attended an outdoor activity day.
- 40 took part in walking.
- 18 took part in sailing.
- 3 did neither activity.
One of the people who walked is chosen at random.
Find the probability that this person also sailed. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{11}{40}\) oe | 5 | B3 for walk [only] = 29, walk and sail = 11 or B2 for walk and sail = 11 or M1 for 40 + 18 + 3 – 50 oe M1 for answer \(\frac{n}{40}\) or \(\frac{11}{k}\) OR M1 for 40 + 18 + 3 – 50 oe B2FT for correctly completed Venn diagram with \(40 - x\), \(x\) [their 11], \(18 - x\), [3] correctly placed FT their \(x\) (can be algebraic or \(x\) is an integer \((0 \lt x \lt 18)\) or B1FT for attempt at Venn diagram with \(40 - x\) or \(18 - x\) or 3 correctly placed FT their \(x\) (can be algebraic or \(x\) is an integer \(0 \lt x \lt 18)\) M1 for answer \(\frac{n}{40}\) or \(\frac{11}{k}\) | Accept dec or % equivalents (3 figures) 0.275 or 27.5 % isw cancelling, conversion to other forms For B3 and B2 11 must be identified for both walk and sail M1 implied by 11 seen where \(0 \lt n \lt 40\) and \(11 \lt k \lt 50\) Check previous working for signs of cancelling e.g. \(\frac{18}{40} = \frac{9}{20}\) gets M1 M1 implied by 11 seen For B2 or B1, condone omission of universal set rectangle where \(0 \lt n \lt 40\) and \(11 \lt k \lt 50\) Check previous working for signs of cancelling e.g. \(\frac{18}{40} = \frac{9}{20}\) gets M1 |