Edexcel IGCSE Math A 1.5.HB Venn diagrams with set counts

Practise Venn-count questions by filling each region from totals and solving for unknowns before answering count notation.

Exam points

Complete each Venn diagram region from totals, intersections and subset counts.
Form and solve an equation for x before finding a required Venn diagram region.
Interpret n(A ∪ B), n(A ∩ C) or complements by adding the correct regions.

[Maximum number: 4]

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.

Figure for Question (a) — Edexcel IGCSE Math A Higher

[ 3 ]

(b)

Find

[ 1 ]

(i)

$\mathrm{n}\left(G^{\prime} \cap C\right)$

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

[ 1 ]

Final answer:
$n(G'\cap C)=35$

Follow through from the candidate's Venn diagram. If these three parts are given as probabilities, mark the first one incorrect but award later marks if the numerator is correct.

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1.5.HB Venn diagrams and numbers of elements question 1

Question (a)

Question (b)

Question (i)