Please respond!!!

Question

PLEASE ANSWER ASAP THANK YOU!!

If a rifleman averages 8 hits out of 10 shots at a target, what is the probability that he will hit the target in 3 out of 4 shots?

show work please

Answer 1

If he hits 8 out of 10 shots on average, that means that his probability of success is ⁸/₁₀, or ⁴/₅. If we assume that this probability remains that same with each shot, i.e., that the outcome of each shot is independent of any prior shots, then this will be a binomial random variable.

The probability mass function for a binomial random variable is

P(X = x) = (_nC_x) · p^x · (1 - p)^{n - x}, where x is the number of successes, and n is the number of attempts.

So we can now plug in all of our information:

P(X = 3) = (₄C₃) · (0.8)³ · (0.2)^{4 - 3} = 0.4096.