JAMB 1993 · UME · Q50

Probability

The chances of three independent events $X$ , $Y$ and $Z$ occurring are $\frac12$ , $\frac23$ and $\frac14$ respectively. What is the chance of $Y$ and $Z$ only occurring?

Worked solution (try it first)

" $Y$ and $Z$ only" means $Y$ happens, $Z$ happens and $X$ does not.
$X$ fails with probability $1 - \frac12 = \frac12$ .
The events are independent, so multiply: $\frac12 \times \frac23 \times \frac14 = \frac{2}{24}$ .
So the probability is $\frac{1}{12}$ , option C.

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