JAMB 2000 · UME · Q41

Probability

$X$ and $Y$ are two events. The probability of $X$ or $Y$ is 0.7 and the probability of $X$ is 0.4. If $X$ and $Y$ are independent, find the probability of $Y$ .

Worked solution (try it first)

Let $P(Y) = p$ .
For independent events, $P(X \cap Y) = P(X) \times P(Y) = 0.4p$ .
Use $P(X \cup Y) = P(X) + P(Y) - P(X \cap Y)$ : $0.7 = 0.4 + p - 0.4p$ .
So $0.6p = 0.3$ and $p = 0.5$ , option B.

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