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Unformatted text preview: 2.21 Wch 11.1 = 6 sightseeing tours each available on 11.2 = 3 different days, the multiplication
rule gives 11.111.2 : = 18 ways for a person to arrange a tour. 2.28 With 11.1 : 5 diiferent manufacturers, 112 : 3 different preparations, and 113 : 2
different strengths, the generalized multiplication rule yields 111112103 : (5)(.‘3)(2) : 30
different ways to prescribe a drug for asthma. 2.33 Since the ﬁrst digit is a 5, there are 11.1 = 9 possibilities for the second digit and then
11; = 8 possibilities for the third digit. Therefore, by the multiplication rule there are
11.111.2 2 (9X8) 2 72 registrations to be checked. m; 2.53 S : {$10,$25,$100} with weights 275/500 : 11/20, 150/500 : 3/10, and 75/500 :
3 / 20, respectively. The probability that the ﬁrst envelope purchased contains less than
$100 is equal to 11/20 + 3/10 : 17/20. 2.56 Consider the events
B: customer invests in tax—free bonds,
111’: customer invests in mutual funds. (a) P[B 051) = 13(8) + P151) — P(B r151) = 0.6 + 0.3 — 0.15 = 0.75.
(b) P(B’ o 51') : 1 — P(B o .11) : 1 — 0.75 : 0.25. 2.58 (a) Let A = Defect in brake system; B = Defect in fuel system; PM U B) 2 PM) ——
13(3) — MA o B) = 0.25 + 0.17 — 0.15 = 0.27. (b) P(N0 defect):1—P[AUB):1—0.27:0.73.
1V; *1”
20? (a) 0.32;
(b) 0.08; {c} ofﬁce or den. 2.70 [3.) 0.02 + 0.30 = 0.32 = 32%;
(b) 0.32 + 0.25 + 0.30 : 0.32 : 37%; (c) 0.05 + 0.00 + 0.02 : 0.13 : 13%;
(d) 1 — 0.05 — 0.32 : 0.03 : 03%. 2.78 P[S  A) : 10/18 : 5/9. 2.79 Consider the et‘ents:
M: a, person is a, male;
3: EL person hes a, set.ondstrj.I ednoetion;
C: a person has a, college degree. (3,) P191  is) = 29/19 = 14/39;
(b) PH?” 91”) = 95/112. LEIJthLJlJ'LLIJ 4.134 J_l'JLI_J.'L JIJLIJ 444. LLthlJII'LIJ. h 2.80 Consider the events:
A: a person is experiencing hypertension,
B: a person is a hast’3I smoker,
C: a person is a nonsnioker. (a) P(A  B) : 39/49;
(b) P(C  A“) : 49/93 : 19/31. 2.84 Consider the events:
C: an oil change is needed,
F: an oil ﬁlter is needed. [a] P[F  o) = W“? : [L14 — use. ch'} ass —
P on? .
(bl Pic i F) : lam} : % Z 0'35 2.88 Deﬁne
H: head of household is home,
C: a change is made in long distance carriers.
P(H ﬂ 0) = P(H)P(C  H) = (0.4)(03) = 0.12. 2.89 Consider the events:
A: the doctor makes a correct diagnosis. B: the patient sues.
P(A’ DB) 2 P[A’)P[B  A“) = [0.3)[0.9) = 02?. 2.101 Consider the events:
C: an adult selected has cancer,
D: the adult is diagnosed as having cancer.
13(0) : 0.05, P[D  C) : 0.78, PIC“) : 0.95 and P(D  C”) : 0.06. So, P[D) :
P(C H D) —— P(C’ H D) : (0.05)(0.78) + (0.95)(0.06) : 0.096. 2.103 P(C  D) = = = 0.40625. 2.108 Consider the events:
A: a customer purchases latex paint,
A’ : a customer purchases semigloss paint, B: a. customer purchases rollers. _ PLB  .AthLAJ _ (Dﬁﬂﬂﬂfﬁ) _ H
P(A I B) _ PEIB  4)PEI4jJ+P{B  A’jPLA’) — (0.60){0.75jn+(o.25){0.3o) — 0'85" ...
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 Spring '11
 Hulett

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