waecmaths question:
The probability that John and James passes an examination are $\tfrac{3}{4}$ and $\tfrac{3}{5}$ respectively. Find the probability of both boys failing the examination.
Option A:
$\tfrac{1}{10}$
Option B:
$\tfrac{3}{10}$
Option C:
$\tfrac{9}{20}$
Option D:
$\tfrac{11}{20}$
waecmaths solution:
$\begin{align} & \Pr (John)=\frac{3}{4} \\ & \Pr (John)'=1-\frac{3}{4}=\frac{1}{4} \\ & \Pr (James)=\frac{3}{5} \\ & \Pr (James)'=1-\frac{3}{5}=\frac{2}{5} \\ & \Pr (John\text{ and }James\text{ }failing)'=\frac{1}{4}\times \frac{2}{5}=\frac{2}{20}=\frac{1}{10} \\\end{align}$
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