Question

Hit probability. A and B are shooting at the same target independently with probabilities 0.6 and 0.15 of hitting it. Find (a) the probability that the target is hit by either A or B (b) the probability that the target is hit by A knowing that it is hit

Answer 1

(a) The probability is 0.66

(b) The probability is 0.9091

Explanation:

The probability that the target is hit by either A or B is calculated as the sum of the probability that the target is hit by A and the probability that the target is hit by B less the probability that A and B happens, as:

P = 0.6 + 0.15 - 0.6(0.15) = 0.6 + 0.15 - 0.09 = 0.66

On the other hand, the probability that the target is hit by A knowing that it is hit is calculated as:

P(A/H) = P(A∩H)/P(H)

Where P(H) is the probability that the target is hit by either A or B and P(A∩H) is the probability that the target is hit by A.

So,

`P(A/H)=(0.6)/(0.66)=0.9091`