Question

n a survey of 331 customers, 66 say that service is poor. You select two customers without replacement to get more information on their satisfaction. What is the probability that both say service is poor?

Answer 1

Answer:

3.93% probability that both say service is poor

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The customers are chosen without replacement, and the order in which they are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

What is the probability that both say service is poor?

Desired outcomes:

Two saying it is poor, from a set of 66. So

$D = C_{66,2} = \frac{66!}{2!(66-2)!} = 2145$

Total outcomes:

Two customers from a set of 331. So

$T = C_{331,2} = \frac{331!}{2!(331-2)!} = 54615$

Probability:

$p = \frac{D}{T} = \frac{2145}{54615} = 0.0393$

3.93% probability that both say service is poor