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.

$\frac{1}{54}$

$\frac{41}{54}$

$\frac{20}{27}$

$\frac{13}{54}$

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) = $\frac{13}{54}$

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The probabilities that Atta and Tunde will hit a target in a shooting contest are 16\frac{1}{6} and 19{1}{9} respectively. Find the probability that only one of them will hit the target.