June 2022 Paper 2 Q4
4 A survey of university students revealed that
- 31% have a part-time job but do not play competitive sport.
- 23% play competitive sport but do not have a part-time job.
- 22% do not play competitive sport and do not have a part-time job.
(a) Show this information on a Venn diagram. [2]
A student is selected at random.
(b) Determine the probability that the student plays competitive sport and has a part-time job. [2]
| Scheme | Marks | AO |
|---|---|---|
 | M1 A1 | 1.1 1.1 |
| [2] |
Notes
M1: Venn diagram with 2 overlapping regions and 0.22 correctly placed; condone incorrect or no labelling
A1: all probabilities or percentages correctly placed and correctly labelled; ignore values in intersection
allow if no box drawn
if labels are eg \(A\) and \(B\), \(A\) and \(B\) need to be defined
| Scheme | Marks | AO |
|---|---|---|
| \(0.31 + 0.23 + \mathrm{p}(J \cap S) = 1 - 0.22\) oe | M1 | 1.1a |
| 0.24 oe isw | A1 | 1.1 |
| [2] |
Notes
M1: may be implied by correct answer or by 24%
A1: do not allow 24%