Problem 50E

Committee A company that has 200 employees chooses a committee of 15 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected.

(a) Use technology to find the number of ways 15 employees can be chosen from 200.

(b) Use technology to find the number of ways 15 employees can be chosen from 144 nonminorities.

(c) What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)?

(d) Does your answer to part (c) indicate that the committee selection is biased? Explain your reasoning.

Solution 50E

Step1 of 5:

The total number of employees in a committee= 200.

The number of employes chosen to represent employee retirement issues = 15.

Here our goal is:

a). We need to find the number of ways 15 employees can be chosen from 200.

b). We need to find the number of ways 15 employees can be chosen from 144 non minorities.

c). When the committee is chosen randomly, then we need to find the probability that the committee contains no minorities.

d). We need to check whether the answer to part (c) indicate that the committee selection is biased.

Step2 of 5:

a).

We know that the combination formula and it is given below:

The number of ways 15 employees can be chosen from 200 is:

The value of is obtained by using combination calculator, By substituting ‘n and r’ values.

Therefore,

Step3 of 5:

b).

The number of ways 15 employees can be chosen from 144 non minorities is:

The value of is obtained by using combination calculator, By substituting ‘n and r’ values.

Therefore,

Step4 of 5:

c).

From part (a) we have:

From part (b) we have:

Now, The probability that the committee contains no minorities is:

Therefore, The probability that the committee contains no minorities is 0.0059.

Step5 of 5:

d).

From part (c) we have the probability that the committee contains no minorities is 0.0059. So, the probability of committee contains no minorities is less than 1. Therefore the answer, in

part (c) does not show that the committee selection is biased.