WAEC 2023 · Paper 1 · Q31

If $X$ and $Y$ are two independent events such that $P(X) = \frac{1}{8}$ and $P(X \cup Y) = \frac{5}{8}$ , find $P(Y)$ .

Worked solution (try it first)

Use $P(X \cup Y) = P(X) + P(Y) - P(X \cap Y)$ , and for independent events $P(X \cap Y) = P(X)P(Y)$ .
So $\frac{5}{8} = \frac{1}{8} + P(Y) - \frac{1}{8}P(Y)$ , which gives $\frac{4}{8} = \frac{7}{8}P(Y)$ .
Divide: $P(Y) = \frac{4}{8} \div \frac{7}{8}$
$= \frac{4}{7}$ , option A.