A is targeting B, B and C targeting A. Probability of hitting the target by A,B and C are respectively 2/3,1/2 and 1/3. If A is hit then find the probability B but not C hits A.
Solution follows here:
The probability that A is hit
=> P(X) = P(hit by B but not C) + P(hit by C but not B) + P(hit by both B and C)
= (1/2)(2/3)+(1/3)(1/2)+(1/2)(1/3) = 1/3 + 1/6 + 1/6 = 2/3
Probability that B but not C hits A
=> P(Y) = (1/2)(2/3) = 1/3
Probability that B but not C hits A, given A is hit= P(Y given X) = P(Y)/P(X) = (1/3)/(2/3) = 1/2