Question

Archer A has a success rate of 70% and archer B has a success rate of 60%. An experiment consist of having A try one to hit a balloon, If A fails, then B also gets one try. If the target is hit, what is the probability it was hit by A? I got 35/41, but the correct answer is 35/44, please explain.

Answer 1

Step 1:

P(Target is hit) = P(A success) + [P(A Fail & B Success) = 0.70 +(0.30X 0.60)

= 0.70 + 0.18 = 0.88

Step 2:

P(A success) = 0.70

Step 3:

Let

X = The target is ht by A

Y = The target is hit

By Multiplication Theorem:
P(X/Y) = P(XY)/P(Y)

         = 0.70/0.88

         = 35/44

So,

Answer is:

35/44

         =