Find the indicated probabilities using the geometric distribution, the Poisson d

Question

Find the indicated probabilities using the geometric distribution, the Poisson distribution or the binomial distribution. Then determine if they are unusual. If convenient use the appropriate probably table or technology to find the probability. Assume the probability that you will make a sale on any given telephone cal is 0.18. Find the probability that you (a) make your first sale on the fifth call. make your sale on the first, second or third call, and (c) do not make a sale on the first calls P(make your first sale on the fifth call) = (Round to three decimal places as needed P(make your sale on the first, second, or third call) (Round to three decimal places as needed) P(do not make a sale on the first three calls) (Round to three decimal places as needed) Which of the events are unusual? Select all that apply The event in part (a) 'make your first sale on the fifth call' is unusual The event in part (b) 'make your sale on the first second or third call', is unusual The event in part (c) 'do not make a sale on the first three calls' is unusual None of the events are unusual

Explanation / Answer

a. let A be the event that you made a sale at the fifth call. that means you have failed the first four calls

now probability of success to sale at any call is 0.18 and probability of failure is 0.72

hence P(A) = (0.72)*(0.72)*(0.72)*(0.72)*(0.18) = 0.04837 =0.048

b. probability of making a sale at first call is 0.18

probability of making sale at second call is = (0.72)*(0.18)= 0.1296

probability of making first sale on third call is = (0.72)*(0.72)*(0.18) = 0.093

since three events are mutually exclusive and exhaustive hence the

probability of making sale in first, second or third call is = 0.18+0.1296+0.093 = 0.4026 = 0.403

c. prob (do not make a sale in first three calls) = (0.72)*(0.72)*(0.72) = 0.373

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