Higher June 2017 Paper 2 Q18
18 A school has 86 teachers.
- 42 are male and 44 are female.
- \(\dfrac{1}{3}\) of the male teachers have blue eyes.
- \(\dfrac{1}{4}\) of the female teachers have blue eyes.
(a) \(\xi =\) teachers in the school
M = male teachers
B = teachers who have blue eyes
Complete the Venn diagram. [3 marks]
(b) One teacher who has blue eyes is chosen at random.
Work out the probability that the teacher is male. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
Fully correct diagram | B3 | B2 Two or three correct numbers in correct positions B1 One correct number in correct position |
Additional guidance
| Three correct numbers in correct positions and one missing | B2 |
| Two correct numbers in correct positions and two missing | B2 |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{14}{25}\) or 0.56 or 56% | B1ft | Correct or ft their diagram oe fraction |
Additional guidance
| \(\dfrac{14}{25}\) or 0.56 or 56% always scores B1 | |
| ft answer correct with subsequent incorrect simplification | B1ft |
| Ratio eg 14 : 25 | B0 |
| Expressed only in words eg 14 out of 25 | B0 |
| \(\dfrac{14}{25}\) and 14 out of 25 | B1 |
| \(\dfrac{14}{25}\) seen with change to incorrect decimal or incorrect percentage eg \(\dfrac{14}{25}\) and answer 0.8 | B1 |
| Ignore chance words if \(\dfrac{14}{25}\) seen eg \(\dfrac{14}{25}\) and answer likely | B1 |
| For a ft answer that is only seen as a decimal or %, accept truncation or rounding to at least 2sf |