Question

Suppose that, during the next hour, 20 customers each purchase one cup of coffee. Assume that the customers make their decisions independently, and each customer has a 17% probability of ordering decaffeinated coffee. What is the probability that everyone will order a coffee with caffeine? g

Answer 1

0.0241 or 2.41%

Explanation:

Since each customer has a 17% probability of ordering decaffeinated coffee, the probability of a customer ordering a coffee with caffeine is:

`P(C) = 1-0.17 = 0.83`

If customers make their decisions independently, the probability that all 20 order a coffee with caffeine is:

`P(X=20)=P(C)^(20)\\P(X=20) = 0.83^(20)=0.0241=2.41\%`

The probability is 0.0241 or 2.41%.