The probability of hitting the target with one shot is 0.7 and does not depend on the number of the shot.

The probability of hitting the target with one shot is 0.7 and does not depend on the number of the shot. Find the probability that with 5 shots there will be exactly 3 hits on the target.

The probability of hitting with one shot is p = 0.7.
The probability of a miss q = 1 – p = 1 – 0.7 = 0.3;
According to Bernoulli’s formula, the probability of hitting 3 times with 5 shots will be equal to:
P = C (5,3) * p ^ 3 * q ^ 2;
C (5,3) is the number of combinations of them 5 to 3.
C (5,3) = 5! / (3! * (5 – 3)!) = 5 * 4 / (1 * 2) = 10.
The probability that there will be 3 hits for 5 shots:
P = 10 * 0.7 ^ 3 * 0.3 ^ 2 = 10 * 0.343 * 0.09 = 0.3087.
Answer: The probability that there will be exactly 3 hits is 0.3087.