SOLUTION: A salesman sells a car to one out of 20 customers. What is the probability that he will sell two out of three cars?

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Question 363042: A salesman sells a car to one out of 20 customers. What is the probability that he will sell two out of three cars?
Answer by Theo(13342) About Me  (Show Source):
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the probability that he will sell 1 car is (1/20) = .05

the probability that he will sell exactly 2 out of 3 cars is equal to:

.05 * .05 * .95 * the number of ways this can happen.

the number of ways this can happen is 3! / (2! * 1!) = 3

the general equation for that is n! / (x! * (n-x)!)

n is the total members of the set.
x is the number of members of the set that you draw from.

n is equal to 3 which is the total number of cars that can be sold.
x is equal to 2 which is the number of cars from the total number of cars that this salesmen will sell.

the probability is therefore equal to .05 * .05 * .95 * 3 = .007125

the 3 possible ways are:

he sells the 1st and 2d car but not the 3d.
he sells the 1st and 3d car but not the 2d.
he sells the 2d and 3d car but not the 1st.

since there are 3 possible ways and the probability for each way is the same, then the total probability is 3 * the probability for each way.

the probability for each way is .05 * .05 * .95 (first way) which is the same as .05 * .95 * .05 (second way) which is the same as .95 * .05 * .05 (third way).