12. At lunchtime on Wednesday, a café had 19 customers.
7 of these customers bought a meal and a drink.
2 of these customers did not buy a meal or a drink.
The total number of customers who bought a meal was twice the total number of customers who bought a drink.
(a) Complete the Venn diagram below to show this information. [2]
(b) One of these customers is chosen at random. What is the probability that this customer bought a meal? [2]
Mark scheme (a)
Scheme
Marks
Comments
B2
Answers on diagram take precedence.
For 9 AND 1 in correct position. Do not award B2 if more than one number is shown in the same section. Ignore 2 and 7 duplicated (in the correct place) for this B2.
If B2 not awarded, award B1 for one of the following, provided no sections are blank and values are whole numbers:
‘their 9’ + ‘their 1’ = 10
7 + ‘their 9’ = 2 × (7 + ‘their 1’).
A B1 may be awarded even if more than one number is shown in the same section as long as the total for awarding a B1 is correct.
Mark scheme (b)
Scheme
Marks
Comments
\(\dfrac{16}{19}\) or equivalent. ISW
B2
FT \(\dfrac{\text{’their 9’ + 7}}{19}\) in a fraction < 1, provided Meal only not blank.
If not B2, award B1 for one of the following in a fraction < 1:
a numerator of 16
a numerator of ’their 9’ + 7, provided Meal only section not blank
a denominator of 19
a denominator of ‘their 9’ + ‘their 1’ + 9.
An answer of \(\dfrac{16}{19}\) gains B2 regardless of ‘their Venn diagram’.
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