The probability of hitting a target with one of the two guns is 0.8 and the other 0.9. What is the probability that only one gun will be hit during a salvo?
The probability of hitting the first weapon is p1 = 0.8;
The probability of a miss with the first gun is q1 = 1 – p1 = 1 – 0.8 = 0.2;
The probability of hitting the second weapon is p2 = 0.9;
The probability of a miss with the second gun is q2 = 1 – p2 = 1 – 0.9 = 0.1;
Event A, such that there will be one hole can occur if there was a hit from the first gun, and the second missed or hit from the second gun, and the first missed. These events are inconsistent, so their probability will be equal to the sum of the probabilities.
P (A) = p1 q2 + q1 p2 = 0.8 0.1 + 0.2 0.9 = 0.08 + 0.18 = 0.26.
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