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:

__Solution:__
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**
p(hit by c but not by b) should be 1/3*2/3????

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