Higher June 2022 Paper 2 Q16

EdexcelHigherCurrent spec8 marksSets

16 100 farmers are asked if they have goats (\(G\)), sheep (\(S\)) or chickens (\(C\)) on their farms.

Of these farmers

31 have sheep
53 have chickens
6 have goats, sheep and chickens
11 have sheep and goats
17 have sheep and chickens
18 have goats and chickens
20 do not have any goats, sheep or chickens

(a) Using this information, complete the Venn diagram to show the number of farmers in each appropriate subset. (3)

Blank Venn diagram with three overlapping circles G, S and C inside a universal set rectangle

(b) Find

(i) \(\mathrm{n}(G)\) (1)

(ii) \(\mathrm{n}([G \cup S]')\) (1)

(iii) \(\mathrm{n}(G' \cap C)\) (1)

One of the farmers who has chickens is chosen at random.

Completed Venn diagram: G only 13, S only 9, C only 24, G and S only 5, G and C only 12, S and C only 11, all three 6, outside 20 — Mark scheme (a)

Scheme	Marks
Answer: Fully correct Venn diagram	B1
	B2
	(3)

Mark scheme (b)

Scheme	Marks
(i) 36	B1ft
(ii) 44	B1ft
(iii) 35	B1ft
	(3)

Notes

ft from a diagram where values are present in the required regions

If these 3 parts are given as probabilities, please mark incorrect the first time but award marks from there on if numerator is correct

Mark scheme (c)

Scheme	Marks
\(\dfrac{18}{53}\)	B2ft
	(2)
	(8 marks)

Notes

B2ft: oe 0.33(96…) or 33(.96…)% ft their Venn diagram

(B1 for \(\dfrac{18}{m}\) where \(m \gt 18\) or \(\dfrac{n}{53}\) where \(n \lt 53\) or

for 18 : 53 or other incorrect notation

or B1ft their Venn diagram for

\(\dfrac{\text{``}{18}\text{''}}{m}\) where \(m \gt \text{``}{18}\text{''}\) or \(\dfrac{n}{\text{``}{53}\text{''}}\) where \(n \lt \text{``}{53}\text{''}\))