Probability practice solutions

Prob ppassapa ppassbpb ppasscpc 705 6830 772 708 30

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P(Pass) = P(Pass and A) + P(Pass and B) + P(Pass and C)      [law of Tot. Prob] = P(Pass|A)P(A) + P(Pass|B)P(B) + P(Pass|C)P(C) =(.70)(.5) + (.68)(.30) + (.77)(.2) = .708 30. If the selected student passed the test, what is the probability that the student took the test at  location  B Answer: 5
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.2881 .708 (.68)(.30) P(Pass) B)P(B) | P(Pass Pass) P(B| = = = 31. What is the probability that the selected student took the test at location  and failed?  P(Pass C  and C) = P(Pass C |C)P(C) = (.23)(.20) = .046 Abby, Brenda, and Cameron; three candidates for the presidency of a college’s student body, are  to address a student forum. The forum’s organizer is to select the order in which the candidates  will give their speeches, and must do so in such a way that each possible order is equally likely to  be selected. 32. List the outcomes in the sample space. S  = {ABC, ACB, BAC, BCA, CAB, CBA}, where A=Abby, B=Brenda, C=Cameron. 33. Assign probabilities to the outcomes. Each outcome is equally likely; since there are 6 possible outcomes, the probability of each  is 1/6. 34. What is the probability that Cameron will speak first?  Looking at the possible outcomes we see that “C” is in the first space twice, thus, 2 out of  the 6 outcomes, or 1/3 35. What is the probability that one of the women will speak first?  Again, looking at the possible outcomes, this happens 4 out of the 6, or, 2/3 (Cameron is a  man) 36. What is the probability that Abby will speak before Cameron does?  Looking at the outcomes, ‘A’ comes before ‘C’ 3 out 6; thus the probability is 1/2 A survey of a magazine’s subscribers indicates that 50% own a home, 80% own a car, and  90% of the homeowners who subscribe also own a car. What proportion of subscribers Write down the givens: P(H) = .50, P(C) = .80, P(C|H) = .90 37. own both a car and a house? P(C and H) = P(C|H)P(H) = (.90)(.50) = .45 6
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38. own a car or a house, or both?  P(C or H) = P(C) + P(H) – P(C and H) = .80 + .50 - .45 = .85 39. own neither a car nor a house?  P(C C  and H C ) = 1 – P(C or H) = 1 - .85 = .15 7
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