The shooter fires three shots at the target. The probability of hitting a target with each shot is 0.6.

The shooter fires three shots at the target. The probability of hitting a target with each shot is 0.6. What is the probability that the target will be hit by exactly one shot?

Event A is such that the target will be hit with exactly one shot, it is possible if the shooter either hits the first shot and misses with the other two, or hits the second or third shot. The probability of event A is:
P (A) = p * q * q + q * p * q + q * q * p = 0.6 * 0.4 * 0.4 + 0.4 * 0.6 * 0.4 + 0.4 * 0.4 * 0.6 = 0.096 + 0.096 + 0.096 = 0.288.
Answer: 0.288.