WAEC 2012 · Paper 2 · Q2

(a)
Given that $U = \{1, 2, 3, 4, 5, 6, 7, 8\}$ , $X = \{1, 3, 5, 7\}$ and $Y = \{1, 5, 8\}$ , find: (i) $X' \cap Y$ ; (ii) $(X' \cup Y)'$ .
Show the answer
(i) $\{8\}$ ; (ii) $\{3, 7\}$
(b)
The probabilities that Kwakye and Sekyere will pass an examination are $\frac23$ and $\frac34$ respectively. If both of them take the examination, find the probability that exactly one of them would pass.

Worked solution (try it first)

$P(\text{Kwakye fails}) = 1 - \frac23$
$= \frac13$ and $P(\text{Sekyere fails}) = 1 - \frac34$
$= \frac14$ .
Exactly one passes in two ways: Kwakye passes and Sekyere fails, $\frac23 \times \frac14 = \frac16$ .
Or Kwakye fails and Sekyere passes, $\frac13 \times \frac34 = \frac14$ .
Add them: $\frac16 + \frac14 = \frac{5}{12}$ .