Problem

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

Assume the probability that you will make a sale on any given telephone call is 0.14 . Find the probability that you (a) make your first sale on the fifth call, (b) make your sale on the first, second, or third call, and (c) do not make a sale on the first three calls.
(a) $P$ (make your first sale on the fifth call) $=$
(Round to three decimal places as needed.)

Answer

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Answer

Final Answer: The probability that you make your first sale on the fifth call is approximately \(\boxed{0.077}\).

Steps

Step 1 :The problem is asking for the probability of different scenarios given a success probability of 0.14 for each independent trial (telephone call).

Step 2 :For part (a), we are asked to find the probability that the first sale (success) occurs on the fifth call. This is a geometric distribution problem. The probability mass function of a geometric distribution is given by: \(P(X = k) = (1-p)^{(k-1)} * p\) where p is the probability of success on each trial, k is the number of trials until the first success, and \(P(X = k)\) is the probability that the first success occurs on the kth trial.

Step 3 :In this case, p = 0.14 and k = 5.

Step 4 :The calculated probability for the first sale to occur on the fifth call is approximately 0.077. This seems reasonable given the success probability of 0.14. Now, I will round this probability to three decimal places as requested.

Step 5 :Final Answer: The probability that you make your first sale on the fifth call is approximately \(\boxed{0.077}\).

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