The probability that Kofi and Ama hit a target in a shooting competition are \(\frac{1}{6}\) and \(\frac{1}{9}\) respectively. What is the probability that only one of them hit the target?

A.

\(\frac{1}{54}\)

B.

\(\frac{13}{54}\)

C.

\(\frac{20}{27}\)

D.

\(\frac{41}{54}\)

Correct answer is B

P(only one hit target) = P(Kofi not Ama) + P(Ama not Kofi)

P(Kofi not Ama) = P(Kofi and Ama') = \(\frac{1}{6} \times \frac{8}{9} = \frac{8}{54}\)

P(Ama not Kofi) = P(Ama and Kofi') = \(\frac{1}{9} \times \frac{5}{6} = \frac{5}{54}\)

P(only one hit target) = \(\frac{8}{54} + \frac{5}{54} = \frac{13}{54}\)