The probabilities that Ade, Kujo and Fati will pass an examination are (frac{2}{3}, frac{5}{8}) and (frac{3}{4}) respectively. Find the probability that
(a) the three ;
(b) none of them ;
(c) Ade and Kujo only ; will pass the examination.
Explanation
(a) (P(Ade) = frac{2}{3} ; P(Kujo) = frac{5}{8} ; P(Fati) = frac{3}{4})
(P(text{all three pass the exam}) = frac{2}{3} times frac{5}{8} times frac{3}{4})
= (frac{5}{16})
(b) P(Ade fails) = (1 – frac{2}{3} = frac{1}{3})
P(Kujo fails) = (1 – frac{5}{8} = frac{3}{8})
P(Fati fails) = (1 – frac{3}{4} = frac{1}{4})
P(none passes) = (frac{1}{3} times frac{3}{8} times frac{1}{4})
= (frac{1}{32}).
(c) P(Ade and Kujo only pass) = (frac{2}{3} times frac{5}{8} times frac{1}{4})
= (frac{5}{48})