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 \(\boxed{0.077}\).