= P(1) + P(2) + P(3) (the events are mutually exclusive) <ART FILE="02_17eq03.eps" W="91pt" H="21.343pt" XS="100%" YS="100%"/> = 0.38 + 0.14 + 0.02 = 0.54 2-18. Exercise No Exercise Total Cold 45 155 200 No cold 455 345 800 Total 500 500 1000 a. The probability that an employee will have a cold next year is <ART FILE="02_18eq01.eps" W="150.109pt" H="22.568pt" XS="100%" YS="100%"/> = .20 b. The probability that an employee who is involved in an exercise program will get a cold is <ART FILE="02_18eq04.eps" W="23.779pt" H="20.821pt" XS="100%" YS="100%"/> = .09 c. The probability that an employee who is not involved in an exercise program will get a cold is <ART FILE="02_18eq06.eps" W="22.598pt" H="19.68pt" XS="100%" YS="100%"/> = .31 d. No. If they were independent, then P(C  E) = P(C), but <ART FILE="02_18eq08.eps" W="50.985pt" H="20.314pt" XS="100%" YS="100%"/> = 0.2 Therefore, these events are dependent. 2-19. The probability of winning tonight’s game is <ART FILE="02_19eq02.eps" W="16.86pt" H="19.109pt" XS="100%" YS="100%"/> = 0.6
= 1 – 0.08 = 0.92 2-25. a. Probability = P(K over M) = 0.2. b. Probability = P(K over MB) = 0.4. c. Probability = [P(K over M) and P(MB over K)] or [P(K over MB) and P(M over K)] = (0.2)(0.6) + (0.4)(0.8) = 0.12 + 0.32 = 0.44 d. Probability = [P(K over MB) and P(K over M)] = (0.4)(0.2) = 0.08 e. Probability = P(MB over K) and P(M over K) = (0.6)(0.8) = 0.48 f. No. They do not appear to be a very good team. 2-26. The probability of Dick hitting the bull’s-eye: P(D) = 0.90 The probability of Sally hitting the bull’s-eye: P(S) = 0.95 a. The probability of either Dick or hitting the bull’s-eye: P(D or S) = P(D) + P(S) – P(D)P(S) = 0.90 + 0.95 – (0.90)(0.95) = 0.995 b. P(D and S) = P(D)P(S) = (0.9)(0.95) = 0.855 c. It was assumed that the events are independent. This assumption seems to be justified. Dick’s performance shouldn’t influence Sally’s performance. 2-27. In the sample of 1,000 people, 650 people were from Laketown and 350 from River City. Thirteen of those with cancer were from Laketown. Six of those with cancer were from River City.
PW = poll predicts win PL = poll predicts loss P(W) = 0.50 P(L) = 0.50 P(PW | W) = 0.80 P(PL | W) = 0.20 P(PW | L) = 0.10 P(PL | L) = 0.90 2-49. Let S = successful restaurant U = unsuccessful restaurant PS = predicts successful restaurant PU = model predicts unsuccessful restaurant P(S) = 0.70 P(U) = 0.30 P(PS | S) = 0.90 P(PU | S) = 0.10 P(PS | U) = 0.20 P(PU | U) = 0.80 2-50. Let D = Default on loan; D' = No default; = Loan rejected; R = Loan approved Given: P(D) = 0.2 P(D') = 0.8 P(R | D) = 0.9 P(R' | D') = 0.7 (a) P(R | D') = 1 – 0.7 = 0.3 (b) <ART FILE="DM.02.001.eps" W="160.695pt" H="52.459pt" XS="100%" YS="100%"/> 2-51. (a) F0.05, 5, 10 = 3.33 (b) F0.05, 8.7 = 3.73 (c) F0.05, 3, 5 = 5.41 (d) F0.05, 10. 4 = 5.96 2-52. (a) F0.01, 15, 6 = 7.56 (b) F0.01, 12, 8 = 5.67 (c) F0.01, 3, 5 = 12.06 (d) F0.01, 9, 7 = 6.72 2-53. (a) From the appendix, P(F3,4 6.59) = 0.05, so P(F 6.8) must be less than 0.05.
H="20.809pt" XS="100%" YS="100%"/> 2 <ART FILE="02_56eq03.eps" W="88pt" H="20.809pt" XS="100%" YS="100%"/> .205 3 <ART FILE="02_56eq04.eps" W="86.559pt" H="20.578pt" XS="100%" YS="100%"/> .051 4 <ART FILE="02_56eq06.eps" W="94pt" H="20.117pt" XS="100%" YS="100%"/> .0064 5 <ART FILE="02_56eq05.eps" H="20.809pt" XS="100%" YS="100%"/> .00032 1.0 XP(X) X – E(X) (X – E(X))2 (X – E(X))2P(X) 0.0 –.9985 .997 .326 .41 .0015 0 0 .41 1.0015 1.003 .2056 .153 2.0015 4.006 .2043 .024 3.0015 9.009 .0541 .0015 4.0015 16.012 .0048 .9985 .7948 E(X) = .9985 1.0 2 = (X – E(X))2P(X) = .7948 0.80 Using the formulas for the binomial: E(X) = np = (5)(.2) = 1.0 2 = np(1 – p)
= 5(.2)(.8) = 0.80 The equation produced equivalent results. 2-65. a. n = 10; p = .25; q = .75; <ART FILE="02_57eq01.eps" W="51.378pt" H="19.375pt" XS="100%" YS="100%"/> P(X) X <ART FILE="02_57eq02.eps" W="83.227pt" H="19.375pt" XS="100%" YS="100%"/> .0563 0 <ART FILE="02_57eq03.eps" W="79.766pt" H="19.375pt" XS="100%" YS="100%"/> .1877 1 <ART FILE="02_57eq04.eps" W="83.604pt" H="19.375pt" XS="100%" YS="100%"/> .2816 2 <ART FILE="02_57eq05.eps" W="84.195pt" H="19.375pt" XS="100%" YS="100%"/> .2503 3 <ART FILE="02_57eq06.eps" W="84.195pt" H="19.375pt" XS="100%" YS="100%"/> .1460 4 <ART FILE="02_57eq07.eps" W="83.9pt" .0584 5