Bill and George go target shooting together. Both shoot at a target at the same time. Suppose Bill hits the target with probability 0.7 where as George, independently, hits the target with probability 0.4. Given that exactly one shot hit the target, what is the probability that it was George's shot?

Step-by-step solution

Let the probability, Bill hits the target is (P(B)=0.7 ), and similarly, probability that George hits the target is (P(G)=0.4 ) ( ) Events (B ) and (G ) are independent So, (P(B G)=P(B) P(G)=0.28 ) ( ) The probability that George shot when it is given that exactly one shot hit the target is (= 0.12 0.42+0.12 = 12 54 = 2 9 ) Hence, option (b) is correct.