Bayes Theorem

How would you use bayes theorem to calculate the probabilty of archer B hitting a target, given that one of them has.

Probabilities for the 3 archers:

A=0.6
B=0.3
C=0.5

>>4
This is just an intuitive statement of Bayes' Theorem in this context.

For events X and Y, we define P(X|Y) to be the probability of X occurring, given that Y has occurred.

Bayes': P(X|Y) = [P(Y|X)P(X)]/P(Y)

Let X be the event that B hits the target, and Y be the event that one of them hits the target.

P(X) = 0.3 as given
P(Y) = 0.6 + 0.3 + 0.5 = 1.4
P(Y|X) = P(one has hit, given that B has hit) = 1

So P(X|Y) = 0.3/1.4 = 0.214...