# Big ten yes no yes 849 3645 4494 no 2112 6823 8935

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Big Ten Yes No Yes 849 3645 4494 No 2112 6823 8935 2,961 10,468 13,429 a. P(Neither) = 6823 .51 13,429 = b. P(Either) = 2961 4494 849 .05 13,429 13,429 13,429 + = c. P(Both) = 849 .06 13,429 = 28. Let: B = rented a car for business reasons P = rented a car for personal reasons a. P(B P) = P(B) + P(P) - P(B P) = .54 + .458 - .30 = .698 b. P(Neither) = 1 - .698 = .302 29. a. P(E) = 1033 .36 2851 = P(R) = 854 .30 2851 = P(D) = 964 .34 2851 = b. Yes; P(E D) = 0 c. Probability = 1033 .43 2375 = d. 964(.18) = 173.52 Rounding up we get 174 of deferred students admitted from regular admission pool. Total admitted = 1033 + 174 = 1207 P(Admitted) = 1207/2851 = .42 30. a. P(A B) .40 P(A B) .6667 P(B) .60 = = = b. P(A B) .40 P(B A) .80 P(A) .50 = = = Pac-10

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Introduction to Probability 4 - 9 c. No because P(A | B) P(A) 31. a. P(A B) = 0 b. P(A B) 0 P(A B) 0 P(B) .4 = = = c. No. P(A | B) P(A); the events, although mutually exclusive, are not independent. d. Mutually exclusive events are dependent. 32. a. Single Married Total Under 30 30 or over Total .55 .20 .75 .10 .15 .25 .65 .35 1.00 b. 65% of the customers are under 30. c. The majority of customers are single: P(single) = .75. d. .55 e. Let: A = event under 30 B = event single P(A B) .55 P(B A) .8462 P(A) .65 = = = f. P(A B) = .55 P(A)P(B) = (.65)(.75) = .49 Since P(A B) P(A)P(B), they cannot be independent events; or, since P(A | B) P(B), they cannot be independent. 33. a.
Chapter 4 4 - 10 Cost/Convenience Other .204 .307 .511 .039 .024 .063 .461 .539 Reason for Applying 1.00 Quality Full Time Part Time .218 .208 .426 Total b. It is most likely a student will cite cost or convenience as the first reason - probability = .511. School quality is the first reason cited by the second largest number of students - probability = .426. c. P(Quality | full time) = .218/.461 = .473 d. P(Quality | part time) = .208/.539 = .386 e. For independence, we must have P(A)P(B) = P(A B). From the table, P(A B) = .218, P(A) = .461, P(B) = .426 P(A)P(B) = (.461)(.426) = .196 Since P(A)P(B) P(A B), the events are not independent. 34. a. P(O) = 0.38 + 0.06 = 0.44 b. P(Rh-) = 0.06 + 0.02 + 0.01 + 0.06 = 0.15 c. P(both Rh-) = P(Rh-) P(Rh-) = (0.15)(0.15) = 0.0225 d. P(both AB) = P(AB) P(AB) = (0.05)(0.05) = 0.0025 e. P(Rh O) 0.06 P(Rh O) 0.136 P(O) 0.44 − ∩ = = = f. P(Rh+) = 1 - P(Rh-) = 1 - 0.15 = 0.85 P(B Rh+) 0.09 P(B Rh+) 0.106 P(Rh+) 0.85 = = =

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Introduction to Probability 4 - 11 35. a. The joint probability table is given. Occupation Male Female Total Managerial/Professional 0.17 0.17 0.34 Tech./Sales/Admin. 0.10 0.17 0.27 Service 0.04 0.07 0.12 Precision Production 0.11 0.01 0.12 Oper./Fabricator/Labor 0.10 0.03 0.13 Farming/Forestry/Fishing 0.02 0.00 0.02 Total 0.54 0.46 1.00 b. Let MP = Managerial/Professional F = Female P(MP F) .17 P(MP F) .37 P(F) .46 = = = c. Let PP = Precision Production M = Male P(PP M) .11 P(PP M) .20 P(M) .54 = = = d. No. From part (c), P(PP | M) = .20. But, P(PP) = .12, so P(PP | M) P(PP) 36. a. Satisfaction Score Occupation Under 50 50-59 60-69 70-79 80-89 Total Cabinetmaker .000 .050 .100 .075 .025 .250 Lawyer .150 .050 .025 .025 .000 .250 Physical Therapist .000 .125 .050 .025 .050 .250 Systems Analyst .050 .025 .100 .075 .000 .250 Total .200 .250 .275 .200 .075 1.000 b. P(80s) = .075 (a marginal probability) c. P(80s | PT) = .050/.250 = .20 (a conditional probability) d. P(L) = .250 (a marginal probability) e. P(L Under 50) = .150 (a joint probability) f. P(Under 50 | L) = .150/.250 = .60 (a conditional probability) g. P(70 or higher) = .275 (Sum of marginal probabilities) 37. a. P(A B) = P(A)P(B) = (.55)(.35) = .19 b. P(A B) = P(A) + P(B) - P(A B) = .55 + .35 - .19 = .71 c. P(shutdown) = 1 - P(A B) = 1 - .71 = .29
Chapter 4 4 - 12 38. Let D = Died F = received follow-up treatment F c = did not receive follow-up treatment a. P(D) = 14 29 .0209 2060 + = b. P(D | F) = 14 .0141 990 = P(D | F c ) = 29 .027 1070 = c. No. P(D | F) = .0141, but P(D) = .0209 d. P(D | F) = 20 .0202 990 = P(D | F c ) = 49 .0458 1070 = e. Based on the data for 54 months after discharge from the hospital, the probability of dying is over twice as high for those not receiving follow-up treatment. I would recommend getting follow-up treatment to a friend.

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