An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5. Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?
A) 0.250
B) 0.500
C) 0.410
D) 0.026

Question

Quizplus · Accepted Answer

The probability of making a sale on any appointment is 1/5.
The probability of not making a sale is 4/5.
Therefore, the probability of making a sale on 3 out of 4 appointments is:
(1/5)^3 x (4/5)^1 x 4C3
= 1/125 x 4/5 x 4
= 16/625
= 0.0256 (rounded)
= 0.026 (to 3 decimal places, as required)
Therefore, the likelihood of the agent selling a policy to 3 out of 4 prospective clients is 0.026, which corresponds to answer choice D.

An Insurance Agent Has Appointments with Four Prospective Clients Tomorrow