WAEC 2011 · Paper 2 · Q6✱

1. Draw a Venn diagram with three overlapping circles, M, A and E, inside a rectangle for the 40 students.
2. Fill in the regions you are given: M only 6, A only 9, M and A only 5, A and E only 2.
3. Let the centre (all three) be $x$.
4. Find the centre. Accounts has 19 students: $9 + 5 + 2 + x = 19$, so $x = 3$.
5. M and E only: Mathematics has 18: $6 + 5 + 3 + (\text{M and E only}) = 18$, so M and E only is 4.
6. E only: Economics has 16: $4 + 3 + 2 + (\text{E only}) = 16$, so E only is 7.

(a)

1. The students who passed at least one subject are $6 + 5 + 9 + 3 + 4 + 2 + 7 = 36$.
2. So $40 - 36 = 4$ students failed all three.

(b)

1. Failing both means passing neither.
2. Passed Mathematics or Economics (or both): $18 + 16 - (4 + 3) = 27$.
3. So $40 - 27 = 13$ failed both, and $\frac{13}{40} \times 100 = 32\frac12\%$.

(c)

1. 19 passed Accounts, so $40 - 19 = 21$ failed it.
2. $P(\text{failed Accounts}) = \frac{21}{40}$.