The probability of hitting the target with one shot is 0.6. Find the probability that with five shots the target

The probability of hitting the target with one shot is 0.6. Find the probability that with five shots the target will be hit – never; less than three times and at least one.

Probability of hitting the target: p = 0.6;
The probability of a miss: q = 1 – p = 1 – 0.6 = 0.4;
The probability that with five shots the target will never be hit:
P5 (0) = q ^ 5 = 0.4 ^ 5 = 0.01;
The probability that with five shots the target will be hit once:
P5 (1) = C (5.1) * p ^ 1 * q ^ 4 = 5 * 0.6 ^ 1 * 0.4 ^ 4 = 0.077;
The probability that with five shots the target will be hit twice:
P5 (2) = C (5.2) * p ^ 2 * q ^ 3 = 10 * 0.6 ^ 2 * 0.4 ^ 3 = 0.2304;
The probability that with five shots the target will be hit less than 3 times:
P5 (<3) = P5 (0) + P5 (1) + P5 (2) = 0.01 + 0.077 + 0.2304 = 0.3174;
The probability that the target will be hit at least once:
P5 (> 0) = 1 – P5 (0) = 1 – 0.01 = 0.99.
Answer: 0.01; 0.3174; 0.99.