Question

To pass a certain marksmanship test, an individual is required to shoot at a target until he hits it six times. He is judged on the number of trials that are necessary to achieve this. If the probability of his hitting a target on any trial is 0.25, what is the probability that he requires 18 shots?

Answer 1

The probability that he requires 18 shots is 0.04785

Explanation:

To answer this, we shall be using the negative binomial distribution

From the question;

P = 0.25 , r = 6

q will be 1-p = 1-0.25 = 0.75 Which is the probability of missing a target on any trial

P(X = 18) = (18-1)C(6-1) (0.25)^6 (0.75)^(18-6)

P(X = 28) = 17C5 (0.25)^6 (0.75)^12) = 0.04785