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.
- \(\frac{1}{54}\)
- \(\frac{41}{54}\)
- \(\frac{20}{27}\)
-
\(\frac{13}{54}\)
The correct answer is: D
Explanation
\(P(A)=\frac{1}{6},P(T)=\frac{1}{9}\)
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) = \(\frac{13}{54}\)