In a shooting test, the probabilities of hitting the target are 1/2 for A, 2/3 for B and 3/4 for C. If they fire at the same target, what is the probability that only one of them hits the target?

Probability of A hitting the target: P(A) = $$\frac{1}{2} ​$$​​

Probability of B hitting the target: P(B) = $$\frac{2}{3}$$​​

Probability of C hitting the target: P(C) = $$\frac{3}{4}$$​​

Probability (A hit the target) =1/2
=> Probability (A miss the target) = 1-1/2 = 1/2 Probability (B hit the target) = 2/3
=> Probability (B miss the target) = 1 - 2/3 = 1/3 Probability (C hit the target) = 3/4
=> Probability (C miss the target) = 1 - 3/4 = 1/4
.. The probability that only one hit the target = (1/2 × 1/3 × 1⁄4) + (1/2 × 2/3 x 1/4)+(1/2 × 1/3 × 3/4) = 1/24 + 2/24 + 3/24 = 1/4 ​