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Probability low to charge that instead of using random selection

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A certain company reduced its management staff from 20 managers to 16. The company claimed that four managers were randomly selected for job termination. However, the four managers chosen are the four oldest managers among the 20 that were employed. Answer the questions below.

a. Find the probability that when four managers are randomly selected from a group of 20, the four oldest are selected ______________(type as an integer or a simplified fraction.

b. Is that probability low enough to charge that instead of using random selection, the company actually fired the oldest employees?

(A). Yes, the probability is low enough, therefore, it is possible that the oldest employees were randomly selected.
(B. )No, because it would not be unusual to fire the oldest managers, given that they were randomly selected for termination.
(C.) No, the probability is not low. Each manager had an equal chance of being fired.
(D.) Yes, because it would be unusual to fire the oldest managers, if they were really randomly selected for termination.

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Solution Preview

a) There are a total of 20 managers, Thus there are a total of (20 C 4) = 4845 ways ...

Solution Summary

The probability low enough to charge that instead of using random selection is determined.

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Probability

James Choi, David Laibson, and Brigitte Madrian conducted an experiment to study the choices made in fund selection. Suppose 100 undergraduate students and 100 MBA students were selected. When presented with four S&P 500 index funds that were identical except for their fees, undergraduate and MBA students chose the funds as follows

Student Group
Fund Undergraduate MBA
Lowest Cost Fund 19 19
Second Lowest Cost Fund 37 40
Third Lowest Cost Fund 17 23
Highest Cost Fund 27 18

If a student is selected at random, what is the probablitiy that he or she

a. Selected the lowest or second lowest cost fund?
b. Selected the lowest cost fund and is an undergraduate
c. Selected the lowest cost fund or is an undergraduate
d. Given that a student is an undergraduate, what is the probability that he or she selected the highest cost fund
e. Do you think undergraduate students and graduate students differ in their fund selection?

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