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: Option B
Explanation
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})