The probability that kebba, Ebou and Omar will hit a target are \(\frac{2}{3}\), \(\frac{3}{4}\) and \(\frac{4}{5}\) respectively. Find the probability that only Kebba will hit the target.
A
\(\frac{2}{5}\)
B
\(\frac{7}{60}\)
C
\(\frac{1}{30}\)
D
\(\frac{1}{60}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Pr(Ebou did not hit the target) = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\) = Pr(E'), Pr(Omar did not hit the target) = 1 - \(\frac{4}{5}\) = \(\frac{1}{5}\) = Pr(O')
Hence the probability that only Kebba will hit the target
= Pr(K) x Pr(E') x Pr(O')
= \(\frac{2}{3} \times \frac{1}{4} \times \frac{1}{5}\)
= \(\frac{1}{30}\)
Source: Myschool Past Questions Archive (Record #45827)