Higher June 2017 Paper 5 Q18
18 In a group of 120 adults, 85 watch football, 78 play a sport and 20 do neither.
Find the probability that an adult chosen at random from those who watch football does not play a sport. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\frac{22}{85}\) oe | 5 | isw conversion to other forms M1 for (85 +78 +20) – 120 oe soi Or for 120 – 20 – 78 oe | For 5 marks accept 0.2588.. or 0.259 or 25.88…% to 25.9% M1 implied by 63 or 22 seen  |
| B2FT for correctly completed diagram with \(85 - x\), \(x\) [their 63], \(78 - x\), 20 correctly placed FT their \(x\) (can be algebraic or \(x\) is an integer \(0 \lt x \lt 78\)) Or B1FT for attempt at Venn diagram with \(85 - x\) or \(78 - x\) or 20 correctly placed FT their \(x\) (can be algebraic or \(x\) is an integer \(0 \lt x \lt 78\)) | For B1, condone omission of rectangle for universal set | ||
| B1 for \(\frac{n}{85}\) or \(\frac{22}{n}\) (both proper fractions) seen | |||