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. Income $60,000 or Below Income Above $60,000 Noncollege Graduate 2040 850 College Graduate 400 710 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 | Ac) = (b) Are the events A and B independent events? Yes No

Explanation / Answer

here from given data ; below is the contingency table:

from above P(A)=1110/4000= 0.2775

P(B)=1560/4000=0.39

P(A n B)=710/4000=0.1775

P(B|A)=710/1110=0.6396

P(B|Ac)=850/2890=0.2941

b)

here as P(A)*P(B)=0.2775*0.39=0.1082

and P(A nB)=0.1775

as P(A)*P(B) and P(A n B) are not equal ; therefore events A and B are not independent.

hence No

Income Non college grads college grads total <$60000 2040 400 2440 >$60000 850 710 1560 Total 2890 1110 4000

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