The probabilities that Atta and Tunde will hit a target in a shooting contest are \(\frac{1}{6}\) and \({1}{9}\) respectively. Find the probability that only one of them will hit the target.

A.

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

B.

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

C.

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

D.

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

Correct answer is D

\(P(A)=\frac{1}{6},P(T)=\frac{1}{9}\)

Probability that only one of them will hit the target = \(P(A)\times P( \bar T ) + P( \bar A )\times P(T)\)

Where \(P( \bar T )\) is the probability that Tunde will not hit the target and \(P( \bar A )\) is the probability that Atta will not hit the target

\(P( \bar T )=1-\frac{1}{9}=\frac{8}{9}\)

\(P( \bar A )=1-\frac{1}{6}=\frac{5}{6}\)

Pr(only one) =\((\frac{1}{6}\times\frac{8}{9}) + (\frac{5}{6} \times \frac{1}{9}) =\frac{4}{27} + \frac{5}{54}\)

\(\therefore\) pr (only one) = \(\frac{13}{54}\)