The probability of hitting the target with one shot is 0.8. The shooter fires 6 shots at the target.

The probability of hitting the target with one shot is 0.8. The shooter fires 6 shots at the target. Determine the probability of 4 hits.

Probability to hit with one shot: p = 0.8.
The probability of a miss: q = 1 – p = 1 – 0.8 = 0.2.
The probability that with 6 shots fired, 4 hits will occur, we determine by the Bernoulli formula:
P (4) = C (6,4) p ^ 4 q ^ (6 – 4), where C (6,4) is the number of combinations of their 6 elements by 4 each.
C (6.4) = 6! / (4! (6 – 4)!) = 5 6 / (1 2) = 15.
P (4) = 15 0.8 ^ 4 0.2 ^ 2 = 0.2458.
Answer: The probability of hitting the target 4 times with six shots is 0.2458.