NECO 2023 · Paper 1 · Q41

Probability & distributions

The probabilities of three events $A$ , $B$ and $C$ occurring are $\frac13$ , $\frac12$ and $\frac23$ respectively. Find the probability that only two of the events will occur.

Worked solution (try it first)

"Only two" means exactly one event fails.
The chances of failing are $\frac23$ for $A$ , $\frac12$ for $B$ and $\frac13$ for $C$ .
$A$ and $B$ only: $\frac13 \times \frac12 \times \frac13 = \frac{1}{18}$ .
$A$ and $C$ only: $\frac13 \times \frac12 \times \frac23 = \frac{2}{18}$ .
$B$ and $C$ only: $\frac23 \times \frac12 \times \frac23 = \frac{4}{18}$ .
The three cases can't happen together, so add: $\frac{1 + 2 + 4}{18} = \frac{7}{18}$ , option E.

Report a problem with this question