The personnel department of Franklin National Life Insurance compiled the accomp
ID: 3151611 • Letter: T
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.)
(b) Are the events A and B independent events?
YesNo
Income$60,000 or Below Income
Above $60,000 Noncollege Graduate 2000 810 College Graduate 450 740
Explanation / Answer
There are 2000+810+450+740 = 4000 employees here.
a)
i.
From the table,
P(A) = (450+740)/4000 = 0.2975 [ANSWER]
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ii.
From the table,
P(B) = (810+740)/4000 = 0.3875 [ANSWER]
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iii.
From the table,
P(A n B) = 740/4000 = 0.185 [ANSWER]
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iv.
Hence,
P(B|A) = P(A n B)/P(A) = 0.185/0.2975 = 0.621848739 [ANSWER]
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v.
Hence,
P(B|Ac) = P(B n Ac)/P(Ac)
= [P(B) - P(A n B)]/(1-P(A))
= (0.3875-0.185)/(1-0.2975)
= 0.288256228 [ANSWER]
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b)
As P(B|A) =/= P(B) in part a, then NO, THEY ARE NOT INDEPENDENT. [ANSWER]
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