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 What is the probability that a manager has a college degree? What is the probability that a manager does not have a college degree? What is the probability that a manager is fair and has a college degree? What is the probability that a manager is fair or has a college degree? What is the probability that a manager is not fair and does not have a college degree? Are the events "fair" and "some college" mutually exclusive? Explain.

Explanation / Answer

a) The corresponding total to college degree is 79, And total frequency is 160,

Therefore,

Prob(college degree) = 79/160=0.4938

b) To find probabilty of not having degree means it is complement of probability of having degree

Therefore,

Prob( not have college degree) = Prob(college degree)c

= 1 - P(college degree)

= 1 - 0.4938

= 0.5063

c) The correspong value of fair and college degree is 49.

Therefore,

Prob( fair and college degree) = 49/160 = 0.3063

d) The correspong total of fair is 87,

Therefore,

Prob( fair) = 87/160 = 0.5438

Now,

Prob( Fair or college degree) = Prob(fair) + Prob( college degree) - Prob(fair and college degree)

= 0.5438 + 0.4938 - 0.3063

= 0.7313

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