Sets 3
3 marks · EasyThe Venn diagram below shows information about a class of 50 students and whether they have a pet cat (C) or a pet dog (D).
How many students have only a pet cat?
What is the probability that a student chosen at random has both a pet cat and a pet dog?
How many students do not have a pet cat or a pet dog?
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(a) 10 · must show Labelled correctly as only C
(b) 0.14 · must show Computes 7/50
(c) 20 · must show Identifies region outside both sets
Common mistakes: Misreading diagram labels
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Marking points
A1 (a) · 1 mark · Correctly identifies 10 students with only a cat (from C but not also D).
A2 (b) · 1 mark · Calculates P(C ∩ D) = 7/50 = 0.14.
A3 (c) · 1 mark · Identifies 20 students in neither set (outside C or D).
Worked solution
a) Only a cat: 10
b) Both: 7/50 = 0.14
c) Neither: 20