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The probabilities that Ago, Sulley and Musa will gain admission to a certain university are $\frac{4}{5}, \frac{3}{4}$ and $\frac{2}{3}$ respectively. Find the probability that :

(a) none of them will gain admission:

(b) only Ago and Sulley will gain admission.
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$p(A g o)=\frac{4}{5} ; p(\text { Sulley })=\frac{3}{4} ; p(\text { Musa })=\frac{2}{3}$
(a) p(none admitted) $=p\left(A g o^{\prime}\right) \times p\left(\right.$ Sulley $\left.^{\prime}\right) \times p\left(\right.$ Musa $\left.^{\prime}\right)$
$=\frac{1}{5} \times \frac{1}{4} \times \frac{1}{3}$
$=\frac{1}{60}$
(b) $p$ (Ago and Sulley admitted only) $=p($ Ago $) \times p($ Sulley $) \times p\left(\right.$ Musa $\left.^{\prime}\right)$
\begin{aligned} &=\frac{4}{5} \times \frac{3}{4} \times \frac{1}{3} \\ &=\frac{1}{5} \end{aligned}
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