Question

If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by P(x) = p(1 - p)* where p is the probability of success on any one trial. Assume that the probability of a defective computer component is 0.15. Find the probability that the first defect is found in the eighth component tested. (Round answer to four decimal places.) P(8) = Points possible: 1 Unlimited attempts. Score on last attempt: 0. Score in gradebook: 0 Message instructor about this question

Answer 1

Solution :

Given that, the probability of success on any one trial p = 0.15 , x = 8

=> In a geometric distribution, the probability of getting the first success on the xth trial is given by

P(X = x) = p*(1 - p)^(x - 1)

=> P(8) = P(X = 8)

= 0.15*(1 - 0.15)^(8 - 1)

= 0.0481

=> The Probability that the first defect is found in the eighth component tested is 0.0481