Three shooters shoot a target. The known probability to hit the target of the first, second and third shooter are 0.3, 0.4 and 0.5 respectively. What is the probability that the target is hit from only one shooter?
I try this.
The probabilities that two will not heat the target:
0.7 x 0.6 = 0.42
0.7 x 0.5 = 0.35
0.6 x 0.5 = 0.30
and finally I'm not sure what should i do with those results? suppose have to multiply them?
Best Answer
Split it into disjoint events, and then add up their probabilities:
The overall probability is therefore:
$$\small(0.3)\times(1-0.4)\times(1-0.5)+(1-0.3)\times(0.4)\times(1-0.5)+(1-0.3)\times(1-0.4)\times(0.5)=0.44$$