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MGF 1106-Exam 2 Review-Nicoli Suco (Answers)

MGF 1106-Exam 2 Review-Nicoli Suco (Answers) - MGP 1106...

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Unformatted text preview: MGP 1106 Finite Math Review # 2 E. Nicoli-Suco Name M“‘“In addition to this review, I recommend that you attend all classes, complete and review all homework assignments, and take any steps you consider necessary for yourself to succeed in the course. Evaluate the expression. 1)3! 3.24 1)__6___ Answer: 6 l . 2) 11C2 U" Hi. 2) SS Answer: 55 (“'25: 2 ‘, a" 1g 3) 12% [Li rt L 3) | 7' -—"" = i . Answer: 1 U1 -31 0 l_ \1 ‘_ 4) SP4 6 ' g! ‘3! 4) lZD' Answer: 120 S N) ‘1 : 'fi ' - mp4 gt (2. 5) MO , , - 5;, 74, 4' V . . Answer: 1680 - : 3, q) ‘. (4 \1 6) How many different 4—digit sequences can be formed using the digits 0, 1,...,9 if repetition 6) \ o 5 O 0 0 of digits is allowed? . Answer: 10,000 LO_'_‘P_: _\AL' 39. —= JP— 7) A shirt company has 3 designs each of which can be made with short or long sleeves. There 7) are 5 color patterns available. How many different types of shirts are available from this company? Answer: 30 ’5 chafing X S colors K ; sleevexaCslwri‘loml '30 1 ”W 8) How many different 8-digit sequences can be formed using the digits 0, 1,...,9 if repetition 8) W of digits is allowed? . to ~10. o. ,[O’lbigk Answer: 100,000,000 19 '5 -L h ' “ ' 9) License plates are made using 2 letters followed by 3 digits. How many plates can be made 9) 000 if repetition of letters and digits is allowed? 7 r O -\ 0 ‘ -\¥0 Answer: 676,000 2i 7f.6_' l- ,. '—"' 10) A shirt company has 3 designs each of which can be made with short or long sleeves. There 10) 36—— are 6 color patterns available. How many different types of shirts are available from this company? 3 ' M$ij§ Answer: 36 1‘ Q, — 90L,“ . r X 7— ‘ $ W g" (e 11) If 4 newborn babies are randomly selected, how many different gender sequences are 11) ' 7 possrble. ’7, r 1 r 1 . Answer: 16 "_ “'- "'" “" 2707— 12) How many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and 12) if the sequence may not end in 000? Repetition of digits is allowed. 2b“) 3 40' U3 "NO :3000 .- 50km) '— 19"? Answer: 2997 _...— F I 13) A restaurant offers 8 possible appetizers, 9 possible main courses, and 8 possible desserts. 13) $9;— How many different meals are possible at this restaurant? ‘ (Two meals are considered different unless all three courses are the same). Answer: 576 E ;:L' .3— 14) How many different 4—letter radio station call letters can be made if repeats are allowed 14) I 7 S7 and the first letter must be K. O t 10' u ; Answer: 17,576 _L 2.9 —— ’— 15) How many different 7— digit phone numbers are possible if the first digit cannot be a 0? 15) M Answer: 9,000,000 ZiO 16) How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of 16) digits is not allowed? . "7t , 7g, Answer: 210 ~- . . . . 7" \ loo 17) How many ways can 6 people be chosen and arranged in a straight line if there are 8 17) people to choose from? t; l (i P ’ “"-\ 5 ’— D /‘ Answer: 20,160 g (9 ’ Q'G ) _ V‘. ~, 9"}, ’ 4,-S‘v‘i'3 .. fl’g"— ’-— 18) A musician plans to perform 7 selections. In how many ways can she arrange the musical 18) fly— selections? ‘7te , s" w ~ chi. Answer: 5040 , ‘ “‘ —' ""' ”— 19) A musician plans to perform 4 selections. In how many ways can she arrange the musical 19) 2 Lf selections? Answer: 24 ,1 I E— 3 [A 20) So 20) There are 9 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? 7(_ {“570 .~ C731): I 7;"— 3'64? 21) In a game of musical chairs, 10 children will sit in 9 chairs arranged in a row (one child will 21) w not find a chair). In how many ways can 9 of the children find seats? ~ Answer: 504 at P3 :- / I Answer: 3,628,800 P [0- ID— _ [5/ ’0 a 1 ((0’7): T 22)_’§_©__._ 22) In how many ways can 2 letters be chosen from the set {A, B, C, D, E, F} if order is important and no repeats are allowed? Answer: 30 G ' g— ’— ii: 23) There are 12 members on a board of directors. If they must form a subcommittee of 4 23) members, how many different subcommittees are possible? I Answer: 495 C I ( L ~ 1 7/ i ll % ' .,.—— '~ (I2 “Oi ‘(Z 81‘“ 24) There are 13 members on a board of directors. If they must form a subcommittee of 6 24) I? I (0 members, how many different subcommittees are possible? . ( Answer: 1716 . C ,3 i _. ./ .3.-. g 5 T ...—-H-——"" ' I / . 25) The library is to be given 5 books as a gift. The books will be selected from a list of 27 titles. 25) m) 7 30 If each book selected must have a different title, how many possible selectio?s are there? r .— . I Answer: 80,730 C 5' ' Lil—£7— ; $1.. 87 (99.5} 9L 522/, 5' 26) In a certain lottery, 4 numbers between 1 and 13 inclusive are drawn. These are the 26) I r winning numbers. How many different selections are possible? Assume that the order in which the numbers are drawn is not important. , l Answer: 715 g C .1 a ' 3 ‘ _- '2’ / "— . 03.491"! ”(W 27) How many ways can an IRS auditor select 6 of 8 tax returns for an audit? 27) 2 ? Answer: 28 C ., J I 8‘ ’. 3 Q (as): w 2‘19! 28) Three student representatives are to be chosen from a group "of five students: Andrew, 28) __Q_ Brenda, Chad, Dorothy, and Eric. In how many different ways can the representatives be chosen if two must be male and one female? :1 f 3’. Answer: 6 a C] I 3 CD : g—J: /: I 7(1):?! 1 D - 3 ’7 29) Three student representatives, a president, a secretary, and a treasurer, are to be chosen 29) / 2" i from a group of five students: Andrew, Brenda, Chad, Dorothy, and Eric. In how many different ways can the representatives be chosen if the president must be a woman and the”... secretary and treasurer must be men? ‘ ‘ 'C . .c , C‘sjnwe IL Answer: 12 & l 3 l 2 / p/‘Q S M mev L, 30) Two student representatives, a treasurer and a secretary, are to be chosen from a group of 30) / five students: Andrew, Brenda, Chad, Dorothy, and Eric. In how many different ways can the representatives be chosen if the two must not be the same sex? Answer:12 3C/"2C/ ()6, '3C(: (9+9: /L True; Sec TM 5 5‘6. 31) A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if 31) LII"; O the committee can have at most two girls? Answer: 4620 ways I'oC‘T 1“ IoC3'llCI 4'I0CL.IZC?* :Z(o+[l7o—n_)[email protected]\’.ég) e 210 +— L+LIO +4770 { o 7:41) I I 7rd) 4 (2 7.70) ) A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. 32) 2 cherry, 1 lemon Answer: .1818 33) All lemon Answer: 0 34) All orange Answer: .0061 35) All cherry Answer: .1212 36) One of each flavor Answer: .2182 ofp'zc lifz l = ”‘2 - 3.2 Mi" _'/6§' I My) «séSAV/C on (a 2’ ’W 3.4.... ——"Zf”———‘:’ /a$+' 37) Six students, A, B72, D, E, F, are to give speeches to the class. The order of speaking is p \Q DECABF (d) that A or B will speak first. a) 1 1 1 Answer. —6—, ”7-257;- \ c475 C) determined by random selection. Find the probability that (a) E will speak first (b) that C will speak fifth and B will speak last (c) that the ents will speak in the following order: PE, 9) ‘lP‘t' IPfiPt .L (‘41. spa 00 LPI ’sPS éP __2 2“ \ _ 38) Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birth ay party. They arrive randomly and each person arrives at a different time. In how many ways can they arrive? In how many ways can Jean arrive first and Keith last? Find the probability that Jean will arrive first and Keith will arrive I t. - ’ Answer: 720; 24;% a) 6 P6 ; $955 1‘4 7 o( .-. L a) ———- ; _..—- 6P0 3"7/0 g 0 in) ‘p' .L‘P“ . I .0333 32) 4278/ > 33) _____.___O 34) .Qowé 35) .a/z, 36) iii 37) ‘( f: 7'9 O ‘, _I_ #103 38) P. : l 0:2‘4'I: ZL‘I ‘39) A "group consists of 6 men and 5 women. Five p op e re selected to attend a conference. In how many ways can 5 people be selected from this group of 11? In how many ways can 5 men be selected from the 6 men? Find the probability that the selected group will consist of all men. Answer: 462; 6; —1—- COHCS c WL 77 C3 :— : 9—. C [~th I\ b) 0% ' .— IQ 39) 40) A box contains 21 widgets, 4 of which are defective. If 4 are sold at random, find the 40) probability that (a) all are defective (b) none are defective. . 1 ._68_ c C 2 v0 , “t 3% (48 Answer' 5985’ 171 a) Li : L. ‘3) ‘L‘L c ‘5 ' .——-—v ’r l ‘3,ch SfiSIS z‘c‘,‘ 5935 H9} '7 41) A committee consisting of 6 people is to be selected from eight parents and four teachers. 41) Find the probability of selecting three parents and three teachers. . _8_ c . C Answer. 33 g 3 ‘1 7) 66), L( 21111 5‘0 ’ ¢6 M“ : 1 ._—-—-— 'r A— ’ ._——-— . c, 42% W4 93' ">3 \ 7’ (. 42) If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability that all 5 cards 42) are picture cards. C 1 5 Answer: 102390 l C =, Ell. ' fl : L 33 says 25731420 $47340 33‘1,x% 103,270 43) If you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting 3 43) jacks and 3 aces. Answer: qf—g—fi ; f h— : /—‘ 2544815 31 C (a 0’20} 535810 0215358520 RSWWS 44) To play the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, 44) paying $1 for each five—number selection. If the five numbers picked are the same as the ones drawn by the lottery, an enormous sum of money is bestowed. What is the probability that a person with one combination of five numbers will win? What is the probability of winning if 100 different lottery tickets are purchased? _ 1 _ g [to ( ) Answe" 1,221,759’ 1,221,759 a) V _____,, __‘__—___-— ‘ (9 C ‘J W, 95" ‘45 6 Find the requested probability. 45) A family has five children. The probability of having a girl is %. What is the probability of 45) having no girls? _L ’_l___'__' L ’L : l DleM (M MAS) m 6+! —\- , l 03 \3 Answer:.0313 7' 2 ,7,;1»7a ,/ ”511, .t l 32.. A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the giv 1t. £.“(0 a 46) Exactly one four (5) <1 >| <€JL§ ; S («[646)(,‘lg33 ,l : ,‘COLK: 46) | 6 Answer: .402 I] 3 47) Exactly 2 belong to an ethnic minority. Answer: .1990 . (£35 (1 ’51); CC???) : Ll §(, \OKWXJD‘EOG) 7‘ 411%“? Find the probability of the event. 48) A die is rolled 18 times and two threes come up. Answerzaso (@0317? w: ‘53(.5247Xosqa):.27e5 Solve the problem involving probabilities with independent events. 49) A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow. If the pointer is spu'n once, find the probability it will land on green and then yellow. ‘ Answer: % 9(7) : PU.” = a L , Wan—Ma): a g 2—» (9 3 50) A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow. If the pointer is spun three times, find the probability it will land on green every L time. 7 : E: v _ ‘ 1 IL. ’ ‘ \(é) (a we) pa.) (1163— 2 3 - a»? l ’ Answer: —1— 3 3 27 51) A single die is rolled twice. Find the probability of getting a 3 the first time and a 4 the second time. W. L W) ., i A“ ' 36 . b {9 36 ‘° (9 52) A single die is rolled twice. Find the probability of getting a 3 the first time and a 3 the second time. ‘ : .— PC 3) Z J. L , l .L— Answer: g Two balls are drawn from a bag in which there are 4 red balls and 2 blue balls. The number 53) of blue balls is counted. X z a .‘1 0 Answer: C 4 I S 4‘7" I 0 ui'éo IS 3 x P (a 9 57/ L ,0? 0 .4 3 . tree 1 .53 D '9/ w; ’ film C 2 .07 C , c . a1 a L((L ’6 ’L' 2 ’ 7 / :fl: :J—zJ _/ I ’ f, / , C / r /A\ c If 5 f2 / 5 5 9 6 Z 7 In a certain college, 33% of the physics majors belong to ethnic minorities. Find the probability of the event from a random sample of 10 students who are physics majors. 47) {J‘ifio l 49) L \8 l a. 51) 39 _L 52) 3 é Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability. %our cards are drawn from a deck. The number of red tens is counted. 54) Answer: .___‘_———- (g, 77/6,:00) —-—-——————. a ‘w: 139' 300 :. 9g 19' 50C? 5 37:160.. 2qu 1C1. 50% : (215‘ 940 m . “/c 970323" C 01% RF 51 "l ' 52 ”t 51 ”t I 1.00H5xfio5" ) (J’WK ‘03: '1‘”! (W3: .3113 3 .0273_ _(:) (333 00:?) lvo}9.l¢.08~4 fiour coins are tossed and the number of heads 15 counted. 56) Answer: 0' (L; )L Lam §)q : b " 0615“ .0035 x P )3 0 .0625 (-(f)(.‘$) (5 : Lt, ,S«,(9~S = .93 1 25 . .2 1 f . . : 2 .375 }»("Z’)CI$) (-53 c (9 '35 #95 :5?9 3 .25 . .4 3 ,5)‘ = . , ' 4 .0625 3'(3)(-9)g a Li (1?. S: .35 Liv/t1)( S) (.3') =l‘.0é95'l ; ,OQQY' Three cards are drawn from a deck. The number of kings IS counted. 57) 0 . Answer: /-E"’" ‘ ‘ L132”: ”'3'“: 2 $7,335! Licl ' ‘(5’CQ , L!“ “w : ({S(L Z ,ZOqL 5&63 21(00 , 53C3 zzrtoo 7Z‘ld'o 2— . qu-agfi gm , “32—77 m S?— '5‘ 21 W0 ' C ngo Find the expected value of the random variable in the experiment. 5"» *3 ‘ 58) Three coins are tossed, and the number of a1151s noted. 58) @— 3 g' . 1. f - .\"2 S.— ‘. ififitkggc 91:2 §::5'- :57»? “41")» K-WflJFflSH’ OU+W 8 Z 3? (33C 3) L C 5)\ 2’ g ,, zg‘rs“, 373(- +”>(.IZS)"' o+.'5?$‘+-?§+ _' ._ —— .(7. GM; ,s)s( 33° , x — .qu c ”7/5" 330g 3” 59) Three cards are drawn rom eck without replacement. The number of aces is counted. 59) ' c l ’ g" Answer: .2308 0” 11:6:— C3 .7583‘ I’d-{C(P‘fQCLA ‘26HL 54c 3 56163 .1041 , L‘C2'Lwc" 3- Cs'qsco 9 6.0/30 _:r_____= coon S; 3 3163. 8 ‘; (967%) + [(4%th 2401304; 3400029: “2325’ Find the expected value for the random variable. 6mm (M K4 1” (L665) ‘t-KR) “+ (6’1”)(7. 60)3fl... Answer: 7,-73999991 - 2 q A, ’S L 4-” .155 1— %’L(: IS" 61) z 3 6 9 12 15 (014)} + (NW +Q‘SQC‘I") +(I7Q‘L"’(J6°1))___ 111 P(z) 0.14 0.14 0.36 0.26 0.10 :14; {($11 +- 33% 4' 3-iL+(—§ : Answer: 9.12 11 so) 4— K0381) 62) z 24 26 28 2K; 90%) *0ij file} k("€(p[2$)+£ x62) P(z) 0.23 0.12 0.46 017 008 Answer: 29.18 63) A business bureau gets complaints as shown in the following table. Find the expected 63) number of complaints per day. Complaintsperpay O 1 2 3 4 5 0(D‘l)4— l(.('\+l(.96)+'$(.33) +L{C,lq)fS(JZ) Probab111ty.04 .11 .26 .33 .19 .12 Answer: 2.98 64) For a certain animal species, the probability that a female will have a certain number of 64) offspring in a given year is given in the table below. Find the expected number of offspring per year. Number of Offspring 0 1 2 3 4 Probability .31 .21 .19 .17 .12 0(7),) 1’1630 1,3517} 4’ 3L. (3*) + ”(C. (29 Answer: 1.58 ...
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