SOLUTION: 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.

Question 1019597: 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.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
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:

Number of ways to choose r employees out of n is nCr=n!/(r!(n-r)!).
(a)
number of ways to choose 15 out of 200
= 15C200
=14629416353818682834880
(b)
number of ways to choose 15 out of 144
= 15C144
= 85323087086516197776
(c)
Assuming random selection, probability of choosing 15 non-minority members
=(15C144)/(15C200)
= 0.00583 or <0.6%
(d)
The probability calculated in (c) does not indicate that the committee selection is biased. However, if the same selection is repeated many times, the results in (c) would result 1 time out of 171. Normal interpretation would conclude that it is unlikely that the selection was random. Usual criteria for cut-off is between 1 in 100 or one in 20.
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