Higher June 2025 Paper 3 Q18
18 Magda carried out a survey to find out the drinks that people like.
She asked 100 people if they like coffee (\(C\)) or tea (\(T\)) or hot chocolate (\(H\)).
32 people like all three drinks.
15 people like coffee and hot chocolate but not tea.
43 people like coffee and tea.
39 people like tea and hot chocolate.
67 people like coffee.
58 people like hot chocolate.
5 people like only tea.
One of the people is chosen at random.
Given that this person likes coffee,
| Answer | Mark | Mark scheme |
|---|---|---|
| Venn diagram | C4 | fully correct Venn diagram |
| (C3 | 6 or 7 of the 8 regions correct) | |
| (C2 | 4 or 5 of the 8 regions correct) | |
| (C1 | 2 or 3 of the 8 regions correct) |
Additional guidance
Ignore all entries except the region you are marking for each C mark
Repeated digits in the diagram should be counted as 2 elements
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{47}{67}\) | M1 | for \(\dfrac{47}{b}\) where \(b \gt 47\) or ft \(\dfrac{\text{``}47\text{''}}{b}\) where \(b \gt \text{``}47\text{''}\) or \(\dfrac{a}{67}\) where \(0 \lt a \lt 67\) or ft \(\dfrac{a}{\text{``}67\text{''}}\) where \(0 \lt a \lt \text{``}67\text{''}\) |
| A1 | for \(\dfrac{47}{67}\) oe or ft \(\dfrac{\text{``}47\text{''}}{\text{``}67\text{''}}\) oe |
Additional guidance
Need not be written in correct form at this stage eg could be a ratio 47 : 67
\(\text{``}47\text{''} = \text{``}15\text{''} + \text{``}32\text{''}\)
\(\text{``}67\text{''} = \text{``}9\text{''} + \text{``}11\text{''} + \text{``}32\text{''} + \text{``}15\text{''}\)
Accept any equivalent fraction, decimal form 0.70(14..) or percentage form 70(.14…)%