The personnel department of Franklin National Life Insurance compiled the accomp

Question

The personnel department of Franklin National Life Insurance compiled the accompanying data regarding the income and education of its employees. Let A be the event that a randomly chosen employee has a college degree, and let B be the event that the chosen employee's income is more than $60,000. (a) Find each of the following probabilities. (Round your answers to four decimal places.) P(A) = P(B) = P(A intersection B) = P(B | A) = P(B | A^C) = (b) Are the events A and B independent events? Yes No

Explanation / Answer

total person = 2000 + 820 + 440 + 740 = 4000

a) P(A) = (440 + 740) / 4000 = 0.295

b) P(B) = (820 + 740) / 4000 = 0.39

c) P(A B) = 740 / 4000 = 0.185

d) P(B | A) = P(A B) / P(A) = 0.185 / 0.295 = 0.627

e) P(A) = P(A B) + P(Ac B)

or, 0.295 = 0.185 + P(Ac B)

or, P(Ac B) = 0.11

P(B | Ac) = P(Ac B) / P(Ac) = 0.11 / (1 - 0.295) = 0.156

b) Since, P(B | A) is not equal to P(B), A and B are not independent events

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