Intermediate June 2023 Unit 2 Q10
10. A bus going to a Welsh Heritage conference has 43 people on board.
There are 38 students, 4 tutors and a driver on the bus.
At the conference, each student will attend a session on Language, a session on History or both sessions.
- All the students will attend at least one session.
- 18 students will attend both sessions.
- 25 students will attend the session on History.
- The tutors and driver will not attend either of the sessions.
(a) Complete the Venn diagram below to show this information.
The universal set, ε, contains all of the 43 people on the bus. [3]
The universal set, ε, contains all of the 43 people on the bus. [3]
(b) One of the people on the bus is chosen at random.
What is the probability that this person will attend the session on Language? [2]
What is the probability that this person will attend the session on Language? [2]
| Scheme | Marks | Comments | ||
|---|---|---|---|---|
 | Diagram takes precedence. If ‘notches/tallies’ are used, penalise −1 once. | |||
| 5 AND 18 in correct position. | B1 | Award B0 for one of the following:
| ||
| Total of 25 for History. | B1 | FT ‘their 7’ + ‘their 18’, provided both sections are non-zero and no section is blank. | ||
| Overall total of 43 | B1 | FT ‘their 13’ + ‘their 18’+ ‘their 7’ + ‘their 5’ provided all sections are non-zero and no section is blank. Note: The following answers are awarded
|
| Scheme | Marks | Comments |
|---|---|---|
| For B2 or B1, the numerator and denominator must both be whole numbers. | ||
| \(\dfrac{31}{43}\) or equivalent. ISW | B2 | For B2, accept:
Award B1 for one of the following:
Penalise incorrect notation (e.g. ‘31 in 43’) −1. |