Question

4% of the customers of a car dealership buy the most expensive car in the lot. a sample of five customers is selected. what is the probability that exactly 2 customers in the sample will buy the most expensive car?

Answer 1

Explanation:

that means the probability that one customer is buying the most expensive car is

0.04 (= 4%)

that means the probability that the customer is not buying the most expensive car is

1 - 0.04 = 0.96

the probability of 2 out of 5 buying it and 3 not is

0.04×0.04×0.96×0.96×0.96 = 0.0014155776

now, this probability applies to every combination of 2 out of 5 :

C(5, 2) = 5!/(2! × (5-2)!) = 5!/(2! × 3!) = 5×4/2 = 5×2 = 10

so, the general probability that 2 out of the 5 customers will buy the most expensive cars is

10 × 0.04²×0.96³ = 0.014155776