7. [15 pts] Mosaic Plot Contingency Table Type By Size Co 1.00 big medium sm Tot

Question

7. [15 pts] Mosaic Plot Contingency Table Type By Size Co 1.00 big medium sm Total Count Total % Col % Row 96 0.75 0.50 Computer 20 4 12.506.2543.7562.50 44.4428.5787.50 20.0010.00 70.00 0.25 big Pharmaceutical 12 15.63 15.636.25 37.50 55.5671.4312.50 41.6741.6716.67 0.00 Total 16 32 28.1321.8850.00 We pick two companies from the 32. Define the following events. A-both are computer companies), B = {both are computer companies OR both are pharmaceuticals}, and C- fone is a computer company and one is a pharmaceuticalj. Calculate (a) [6 pts] P(A), P(B), P(C); (b) [6 pts] P(B|A) and P(AB); (c) [6 pts] P(AnB) and P(AnBnC) Show all work.

Explanation / Answer

Question 7

(a) P(A) = Pr(Both are computer companies) = 0.625 * 0.625 = 0.3906

P(B) = Pr(Both are computer company or Both are pharma) = 0.625 * 0.625 + 0.375 * 0.375 = 0.5313

P(C) = Pr(One is compute company and one is pharma) = 2 * 0.625 * 0.375 = 0.4688

(b) P(B l A) = Pr(Both are computer company or both are pharma company given both are computer company) = 1

P(A l B) = 0.625 * 0.625 / (0.625 * 0.625 + 0.375 * 0.375) = 0.7353

(c) P (A B) = Pr(A) as A is subset of B

so, P (A B) = 0.3906

P (A B C) = As there is no common intersection as B and C are both mutually exclusive events.

P (A B C) = 0

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