# Two shooters simultaneously shoot at the target what is the probability that only one shooter

Two shooters simultaneously shoot at the target what is the probability that only one shooter will hit the target if the probabilities of hitting for them are 0.5 and 0.4, respectively.

Hit probabilities for shooters:
p1 = 0.5;
p2 = 0.4.

Let’s find the probabilities of the shooters miss:
q1 = 1 – p1 = 0.5;
q1 = 1 – p2 = 0.6.

Let’s calculate the probability that the first shooter hits and the second one misses:
P (A) = 0.5 * 0.6 = 0.3.

Let’s determine the probability that the second will hit and the first shooter will miss:
P (B) = 0.4 * 0.5 = 0.2.

Events A and B are inconsistent, so we use the addition of probabilities:
P (A + B) = P (A) + P (B) = 0.3 + 0.2 = 0.5.

Answer: The probability of hitting the target by only one of the shooters is 0.5.

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