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.
Explanation
\(p(Ago) = \frac{4}{5} ; p(Sulley) = \frac{3}{4} ; p(Musa) = \frac{2}{3}\)
(a) p(none admitted) = \(p(Ago') \times p(Sulley') \times p(Musa')\)
= \(\frac{1}{5} \times \frac{1}{4} \times \frac{1}{3}\)
= \(\frac{1}{60}\)
(b) p(Ago and Sulley admitted only) = \(p(Ago) \times p(Sulley) \times p(Musa')\)
= \(\frac{4}{5} \times \frac{3}{4} \times \frac{1}{3}\)
= \(\frac{1}{5}\)