Each manager of a Fortune 500 company was rated as being either a good, fair, or

Question

Each manager of a Fortune 500 company was rated as being either a good, fair, or poor manager by his/her boss. The manager’s educational background was also noted. The data appear below.

a. What is the probability that a manager has a college degree?

b. What is the probability that a manager does not have a college degree?

c. What is the probability that a manager is fair and has a college degree?

d. What is the probability that a manager is fair or has a college degree?

e. What is the probability that a manager is not fair and does not have a college degree?

f. Are the events “fair” and “some college degree” mutually exclusive? Explain.

Educational Background Manager H.S. Degree Some College College MS or PhD Total Degree Good 24 39 Fair 87 34 Poor 6 32 43 160 Total

Explanation / Answer

a) from above probability that a manager has a college degree =79/160

b)  probability that a manager does not have a college degree =(160-79)/160 =81/160

c)  probability that a manager is fair and has a college degree =49/160

d)  probability that a manager is fair or has a college degree=(3+15+49+20+24+6)/160=117/160

e)  probability that a manager is not fair and does not have a college degree =(2+8+5+1+9+18)/160=43/160

f) for mutually exclusive events A and B

AnB should be empty set

but here  “fair” and “some college degree” contain 15 candidate.

hence not mutually exclusive.

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