Question

20. A new car salesperson knows that she sells a car to one customer out of 20 who enter the showroom.
Find the probability that she'll sell a car to exactly two of the next three customers.
A. 0.9939
B. 0.0075
C. 0.0071
D. 0.1354

Answer 1

A new car salesperson knows that she sells a car to one customer out of 20 who enter the showroom.

Find the probability that she'll sell a car to exactly two of the next three customers.

A. 0.9939

B. 0.0075

C. 0.0071

D. 0.1354

Solution.

1. Let $A$ be the event of selling a car to a customer. Then, according to the conditions $P(A) = 1 / 20 = 0.05$ and $P(\overline{A}) = 1 - P(A) = 0.95$.

2. Let $B$ be the event of selling a car to two customers out of the next three ones. Then

$$B = \bar{A} A A + A \bar{A} A + A A \bar{A}.$$

As the events $\bar{A} A A, A \bar{A} A, A A \bar{A}$ are incompatible then

$$P(B) = P(\bar{A} A A) + P(A \bar{A} A) + P(A A \bar{A})$$

and

$$P(B) = 3 P(\bar{A} A A) = 3 P(\bar{A}) P(A) P(A) = 3 * 0.95 * 0.05 * 0.05 = 0.007125.$$

Answer: 0.007125.