The probabilities that Ade, Kujo and Fati will pass an examination are \(\frac{2}{3}, \frac{5}{8}\) and...
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) = \(\frac{2}{3} \times \frac{5}{8} \times \frac{1}{4}\)
= \(\frac{5}{48}\)