Most binomial probability calculations required in these exercises can be done by using Table C or the Normal approximation. Your instructor may request that you use the binomial probability formula or software. In exercises requiring the Normal approximation, you should use the continuity correction if you studied that topic.
5.39 The geometric distribution.
Generalize your work in Exercise 5.38. You have independent trials, each resulting in a success or a failure. The probability of a success is on each trial. The binomial distribution describes the count of successes in a fixed number of trials. Now, the number of trials is not fixed; instead, continue until you get a success. The random variable is the number of the trial on which the first success occurs. What are the possible values of ? What is the probability for any of these values?
(Comment: The distribution of the number of trials to the first success is called a geometric distribution.)
5.39
has possible values 1, 2, 3, … , etc. , because we must have failures before the success on the kth trial.