Intermediate November 2022 Unit 1 Q14
14. In a group of 200 people:
- 105 people do not have black hair and do not wear glasses
- 20 people have black hair and wear glasses
- 70 people have black hair.
(a) Complete the Venn diagram below to show this information.
The universal set, \(\varepsilon\), contains all 200 people. [3]
The universal set, \(\varepsilon\), contains all 200 people. [3]
(b) One of these people is chosen at random.
What is the probability that this person wears glasses? [2]
What is the probability that this person wears glasses? [2]
| Scheme | Marks | Comments |
|---|---|---|
 | If ‘notches/tallies’ are used, penalise −1 once. | |
| 20 AND 105 in correct position | B1 | B0 if any other number written in the same section. |
| Total of 70 for Black Hair | B1 | FT ‘their 50’ + ‘their 20’, provided both are non-zero values. |
| Overall total of 200 | B1 | Note: The answer below is awarded B1B0B1.  |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{45}{200}\) or \(\dfrac{9}{40}\) or equivalent. ISW | B2 | For B2 or B1, the numerator and denominator must be a whole number. FT \(\dfrac{\text{‘their 20’ + ‘their 25’}}{200}\) provided both sections not blank. Award B1 for one of the following:
Penalise incorrect notation (e.g. ‘45 in 200’) −1. Note:   |