Higher June 2023 Paper 4 Q10
10 100 people were asked whether they had visited France (F) or Spain (S).
- 55 had visited France
- 60 had visited Spain
- 4 had not visited either country.
(a) Complete the Venn diagram.
(b) One of these 100 people is chosen at random.
(i) Write down the probability that this person had visited exactly one of the countries. [2]
(ii) Write down the probability that this person had visited France given that they had also visited Spain. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| F only 36, F and S 19, S only 41, outside 4 (36 19 41 in the circles, 4 outside) | 3 | B2 for 36 or 19 or 41 correctly placed or B1 for the total of F = 55 or for the total of S = 60 or \(F \cap S' + (F \cap S) + F' \cap S = 96\) | Do not accept a blank region as 0, for any marks we need to see a number in each region |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (b)(i) | |||
| \(\frac{77}{100}\) or 0.77 or 77% | 2 | FT \(\frac{their(36 + 41)}{100}\) from their (a) for 2 or 1 marks or M1 for their (36 + 41) or 77 | FT if \(their(36 + 41) \lt 100\) and 0 < fraction < 1 |
| (b)(ii) | |||
| \(\frac{19}{60}\) or 0.316 to 0.317 or 0.32 | 2 | FT \(\frac{their(19)}{their(19 + 41)}\) from their (a) for 2 or 1 marks B1 for 0.19 oe or \(\frac{their\ 19}{k}\) or \(\frac{k}{their\ 60}\) (\(k\) is an integer) | Accept e.g. 32% or 31.6 to 31.7% for 2 marks from their (a) and 0 < fraction < 1 |