5-15 Dr. Arize\'s Class Notes 6. The following table classifies 1000 and type of

Question

5-15 Dr. Arize's Class Notes 6. The following table classifies 1000 and type of employer for whom college graduates by area of concentration in college of employer for whom they went to work after graduation. Type of Employer Public Banking & Electro- Merchand All nics ising Others Accounting Finance Total 100 150 75 120 250 Major 10 Accounting B 60 15 10 General Business B, 20 Humanities B 65 10 20 10 60 70 50 Social B 20 Science 188 Engineering B All others B 30 55 60 110305 Total 115 142 273 165 305 1,000 (a) A graduate is picked at random from this group. Calculate the probability that he or she 1) An accounting major 2) Employed by a banking and finance firm 3) An accounting major employed by a banking and finance firm 4) An accounting major given that he or she was employed by a banking and finance firm 5) An accounting major or an engineering major 6) An accounting major or employed by a banking and finance firm. Evaluate the following probabilities: 1) P (B) (b) 2) (A4) 3) P (B, n A) 4) P (A) P (BIA4) 5) P (A UB) 6) (A4 UA3) (c) Is type of employer independent of area concentration? How do you support your answer mathematically?

Explanation / Answer

a) 1) P(An acounting major) = 100/1000 = 0.1
2) P(Employed by a banking and finance firm) = 142/1000=0.142
3) P(accounting major employed by a banking and finance firm) = 15/1000 =0.015
4) P(accounting major/he or she was employed by a banking and finance firm) =
P(accounting major employed by a banking and finance firm) / P(he or she was employed by a banking and finance firm) = 0.015 / 0.142 = 0.1056
5) P(an accounting major or an engineering major) = P(accounting major) + P(engineering major) - P(accounting major and an engineering major)   
= 0.1 + 250/1000 - 0/1000 = 0.1+ 0.250 = 0.350
6) P(accounting major or employed by a banking and finance firm) =
P(accounting major) + P(employed by a banking and finance firm) - P(accounting major and employed by a banking and finance firm
= 100/1000 + 142/1000 - 15/1000 = 0.227
b)
1) P(B3) = 75/1000 = 0.075
2) P(P(A4) = 165/1000 = 0.165
3) P(B3 and A4) = 10/1000 = 0.010
4) P(A4) * P(B3/A4) = 0.165 * 75/999 = 0.012387
5) P(A4 or B3) = P(A4) + P(B3) - P(A4 and B3) = 0.165 + 0.075 - 0.010 = 0.23
6) P(A4 or A3) = P(A4) + P(A3) - P(A4 and A3) = 0.65 + 0.273 - 0 = 0.923
7) P(A1/B1) = P(A1 and B1) / P(B1) = 60/1000 / 100/1000 = 0.60
c) No, the employer is not independent of area concentration
since P(A1 and B1) = 60/1000 = 0.060 not = P(A) P(B1) = 115/1000 * 100/1000 = 0.0115

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