Foundation June 2023 Paper 2 Q11

AQACurrent spec4 marksSets

11 Here is a Venn diagram.

\(\xi\) = 60 people
H = people who own a gaming headset
W = people who own a smart watch

(a) 15 of the people own a smart watch.

Complete the Venn diagram. [2 marks]

(b) One of the 60 people is chosen at random.

What is the probability that they own both a gaming headset and a smart watch? [1 mark]

He already has £19

He plans to save the rest in two equal amounts over the next two weeks.

He uses this method to work out in pounds how much to save each week.

\(35 - 19 \div 2\)

What is wrong with his method? [1 mark]

Answer	Mark	Comments
8 in W only	B1
21 in (H U W)'	B1ft	ft \(29 -\) their 8 their 8 must be \(\lt 29\)

Mark scheme (b)

Answer	Mark	Comments
\(\dfrac{7}{60}\) or [0.116, 0.117] or [11.6, 11.7]%	B1	oe fraction

Ignore conversion attempt to decimal, fraction or percentage (but not ratio) after correct probability seen

Do not allow eg 7 in 60 or 7 out of 60 unless the correct probability seen

Do not allow ratio

Ignore words if correct probability seen

Mark scheme (c)

Answer	Mark	Comments
Valid explanation	B1	eg needs brackets around \(35 - 19\)

Any calculations shown must be correct
Ignore irrelevant, non-contradictory statements
It gives 25.5 and it should be 8	B1
(It gives the wrong answer,) it should be 8	B1
He shouldn’t divide (by 2) first	B1
He needs brackets around the takeaway	B1
He needs to subtract first	B1
He should do \(35 - 19\) and then divide by 2	B1
\((35 - 19) \div 2\) (may correct the given calculation by adding brackets)	B1
\(\dfrac{35 - 19}{2}\) (implies the brackets)	B1
This gives 25.5 (or 51) when he needs 8 or 16	B1
\(35 - 19 = 16 \quad 16 \div 2 = 8\) (needs to say that this is what he should do)	B0
This gives 25.5 (or 51) which is too much (needs to compare with 8 or 16)	B0
He hasn’t used BIDMAS	B0
It gives the wrong answer	B0
\(35 - 19 \div 2 = 8\)	B0
\(35 - 19 \div 2 = 25.50\)	B0
He needs brackets	B0

15 in W only 21 in (H U W)'	B0 B1
15 in W only 14 in (H U W)'	B0 B1ft