O Level Mathematics — Sets

Two subjects. One overlap.
Every student accounted for.

Numbers, demystified.

O Level Past Paper Style Question

In a class of 40 students:

18 study Mathematics (M)
15 study Biology (B)
12 study both Mathematics and Biology

(a)Draw a Venn diagram to represent this information.✓

(b)Find the number of students who study only Mathematics.✓

(c)Find the number of students who study only Biology.✓

(d)Find the number of students who study neither Mathematics nor Biology.✓

(e)If a student is chosen at random, find the probability that the student studies: (i) Mathematics only (ii) Biology only (iii) Both subjects✓

Solved step by step

n(M) = 18 · n(B) = 15 · n(M ∩ B) = 12

Working

PART —

(a) Place n(M∩B) = 12 in the overlap first, then the given totals around it. —

(b) Only Maths = n(M) − n(M∩B) = 18 − 12 6

(d) Neither = 40 − (6 + 12 + 3) 19

(e) Probability = favourable outcomes ÷ 40 —

(i) Maths only

320

(ii) Biology only

340

(iii) Both

310

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Two subjects. One overlap.Every student accounted for.