geometric distribution

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)x−1

where  is the probability of success on any one trial.

Assume that the probability of a defective computer component is 0.21. Find the probability that the first defect is found in the fifth component tested.(Round answer to four decimal places.)

Answer 1

Hello Jessica B.,

I will get you started. The formula is P(x) = p(1 - p)^{x - 1}. On the right side of the equation, substitute 5 for x and 0.21 for p. Use a calculator to work out the answer.