Three men, P, Q and R aim at a target, the probabilities that P, Q and R hit the target are (frac{1}{2}), (frac{1}{3}) and (frac{3}{4}) respectively. Find the probability that exactly 2 of them hit the target.
-
A.
(1) -
B.
(frac{1}{2}) -
C.
(frac{5}{12}) -
D.
(frac{1}{12})
Correct Answer: Option C
Explanation
(p(P) = frac{1}{2}, p(P’) = frac{1}{2})
(p(Q) = frac{1}{3}, p(Q’) = frac{2}{3})
(p(R) = frac{3}{4}, p(R’) = frac{1}{4})
p(exactly two hit the target) = p(P and Q and R’) + p(P and R and Q’) + p(Q and R and P’)
= ((frac{1}{2} times frac{1}{3} times frac{1}{4}) + (frac{1}{2} times frac{3}{4} times frac{2}{3}) + (frac{1}{3} times frac{3}{4} times frac{1}{2}))
= (frac{1}{24} + frac{6}{24} + frac{3}{24})
= (frac{5}{12})