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})