ECZ 2015 · O-Level Paper 2 · Question 4 — Sets

The Venn diagram shows the number of students who took Business Studies (B), Human Resources (H) and Community Development (C) at Mafundisho College. 100 students took these three courses.

(a) Find

(a(i)) the value of x,[2]

Verified working — step 1

All the Venn regions add to the 100 students.

(a(ii)) the number of students who took Human Resources,[1]

Verified working — step 1

n(H) is every region inside the H circle.

(a(iii)) n(B ∩ C) ∩ H',[1]

Verified working — step 1

(B intersect C) intersect H' means inside both B and C but OUTSIDE H.

(a(iv)) n(B ∪ C) ∩ H'.[1]

Verified working — step 1

(B union C) intersect H' means inside B or C, but outside H.

(b) If a student is chosen at random, what is the probability that the student took

(b(i)) one course,[2]

Verified working — step 1

Exactly one course = the three outer regions.

(b(ii)) at least two courses?[3]

Verified working — step 1

At least two courses = every overlap region.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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