Question

Three shooters shoot at the same target, each of them shoots just once.

The first one hits the target with a probability of 50%, the second one with a probability of 60% and the third one with a probability of 70%. What is the probability that the shooters will hit the target

1. at least once?

2. at least twice?

Answer 1

a) Probability that the shooters will hit the target at least once is computed here as:

= 1 - Probability that none of the shooters hit the target

= 1 - (1 - 0.5)*(1 - 0.6)*(1 - 0.7)

= 1 - 0.5*0.4*0.3

= 0.94

Therefore 0.94 is the required probability here.

b) Probability that the shooters will hit the target at least twice is computed here as:

= Probability that exactly two of them hit the target + Probability that all three hit the target

= 0.5*0.6*(1 - 0.7) + 0.5*0.7*(1 - 0.6) + (1 - 0.5)*0.6*0.7 + 0.5*0.6*0.7

= 0.09 + 0.14 + 0.21 + 0.21

= 0.65

Therefore 0.65 is the required probability here.