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Unformatted text preview: [3:] We wished @working yams far“ W4 ($4.464) ﬁg? ii] I am afﬁnﬁfﬁg worked prgblem fwm “WC Hand moi” F221. :1 L“ It i: («is a:
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mgf1106 85367dougstest®p1. oc/l page of 8. Evaluate each factorial expression.‘ ¢ ” “49““ 320 (8) _§—Si "26 e <o>.[1§)=mo il.’
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9. Usethef_ormula P— — to solve the following question. (/ (11 Mr)!
For a segment of a radio show, a disc jockey can pla 8 r o us. i there ar 11 r®oz select from,[
in how many ways can the program for this segment ‘  W5. Fem The program can be arranged in {g E 2800 ways. I l @l PB, 2&2!
10. In how man distinct we 3 can the letter word®e arranged?
All! we ~—.—~ = 3m 11. You volunteer 0 help drive c II ren at a charity event to the 200, but you can fit only®f the @ hildren present into your van. How manyML/ different $40 ”pf/T 0: Z ildr e fins”: drive? 9“ d”?
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in how ays can a oéegnd t ree wome be formed from a group 0 nine me
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Es / x A committee of three men and three women can be formed from a group of nine men and six women in different ways. 13. esthe"t_heoreticalmprobabiltty formula to solve the following problem. Express the probability as a
fraction reduced to lowest teﬁ'hs) S A 1éisiaaaaraisisi'isé. The set of equally likely outcomes is {1, 2, 3, ﬂ 6, 7, 8, 9,1 0,1 jltz} . Find each
of the following probabilities: 12. Use the formula to ”C (1 _—‘ (A). The probability of rolling a 1 is lg, . (B). The probability of rolling a number less than 12 is 3 r. 3
(C) The probability of roliing a number greater than 3' Is I % 4. (D). The probability of rotting a number greater than 21 is . / mgfi10686367dougstest4a_p11.doc // a e 4 of 5
’ / t/ / C :) 1‘4. A fair coin is tossed three times in succession. The set of equally likely outcomes is
’3':{I§H :_HHTI{J/[email protected]€H,%T91T,}TH TTT}. Give your answer as an integer or a simplified
féction. Find the probability 0 siting: tr}: 8 (A).e <xac9 one taii 3/“ (B) a tail on the third toss (Hint: rememberthis doesn’t mean a tail on the third toss only!) ' i '2 3 4r '3 (a ‘
15. Jim, tan Katrina Kim, Tyrone Larry. and Sirﬁone have aii been invited toa dinner party. They arrive randomly and each persongaﬂrrwﬂeﬁs at a different time. 
6 m (A). in how many ways can they arrive? 5049
(B). in how many ways can Jim arrive first and Simone last? (C). Find the probability that Jim will arrive first and imone iast.
(Round off this probabilitL 46 4 decimal piaces). ‘ J,
16. A group consists oémegnd {Jen woﬁ Three peopie are selected to attend a conference. 2' 5%
(A). in how many ways can three people be selected from this group of thirteen? l5 CS T 2
(B). In how many ways can three women be selected from the seven women? 1 03 : 35 (C). Find the probability that the se ectéd‘g oup will consist of aii women. I i224
(Round off this probability t __4_ decimal aces)“; s tecTe find the rehab Ity fseiecting fou emo rats and threeﬁe blicans. (Rioun ﬁtthbba
o4deCI al places) V (J, 3549 — MC?
1 8. The math depa nt of a coilege ha 5 male professors female professor [12 male teaching
assi tan female teaching assistantgii‘a person Is seie a ran omt e group, In the W that t seiectedw person Is a teaching assistant or a femaie. (Report your answer as a reduced [a X fraction. Emit Fetita 17. A city council consi sjiven Democrats ndéseven Republicans. a fcommitte seven peop
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19. One card is randomly selected from a standard deck of 52 cards. (39
(A). Find the odds [email protected]\@of drawing a spade. The odds are to. _ _
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(B). Find the odds against drawing a four. The odds are to [I Q? (C) Find the odds against drawing a red ace. The odds are a "to L 35.! 9
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lZi l mgf110686367dougstest4a_p11.doc ll page 5 of 5 20. The wi er of a raffle will receive a 78’ 8” Bertram 800 [email protected] affle tickets were sold and you
purchase®ickets what are the odds against your winning the J It“
The odds against “piling the yacht are to . (Remember to “reduce" if possible). . ‘. ,
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......................................................................................................................... 21. (Bonus) if you are giveJ/orcicgnf 4 to 5 tn favor of winning a bet, what Iste probabtittyE‘ mmngﬁte
bet? (Answer as a simplifi (113 c.0n) 9 ‘ﬁig 4 155%. 9 00ch . 7 _ CountinglProbability Unit ,_ _ @  Counting Methods Handout —— Use after 11.3 "ecide whether each of the following is a permutation, combinatidn or a counting princlpie problem; Do notdo
.e actual computation with the formula. but write how you would solve the problem. +— Actwiiig , .1?“ jélitj‘ it“
For example: 10P3 . . . gal/lie . 1. Four identicai prizes are being given to four lucky people. These four winners will be chosen from . * ) i
12 contestants. ow m n wa s can he rizes be awarded? “L 4' ”if”! ‘1 OW“! 5““3 5'” Prﬂe‘g CW 659‘
i204 as iziyfgjq'ﬂz LQXU F'g /E4r/3"X I i 2' ”.45 (car amp/y ,2 C4 —.—. 495 an cai‘crthc'hﬂ‘), 2. License plates are made using 3 letters followed by 3 digits. How m lates can be made if
repetition of letters and digits is allowed? EE‘E'Zé s 17640419  :35 $16,000 —......  1/
3. From the class of 15 students, a President, Vice Piesident, and Treasurer are to be elected. How many .
different sl , f officers are possible, i he may hold more than one office? l5 Fifi/C 3 Order; ”Park”?
in; P3 5 2 30 er Eiﬂiiﬁi’. , 2.;t30 . 4. A delegation [email protected] must be chosen from a college to attend a convention. How many, n at f h f
different delegatiorgc n be chosen if there are eligible students? ,ro Flat 5", “cielegq on ~ 0 9'“ EL ’ 1P 
Candid ‘ ran': 31 or“ lei/(9593}; 25?. Sr (ﬁrsﬁr2'7r‘JICK'iIf/l) '5' 34.7.4 236's} 5. unners compete in a race for which there will 5E: grit and second prizes. in how many ways may  the pri be w'on? ‘ii Pitt? 26”“4—5 ”iiPi» Perm“ “ “#92: (W ,1; gr; 1’“ 2' .
6. License plates are made using Adigits followed by; letters. How many plates can be made if repetition of both letters and digits is allo he ﬁrst digit cannot b_e_ 210?
3 ilﬂ'm’” 5: gig :9eieoO267': 63084 000 W ._,.__‘___—__   r o i ‘ 2 2 t: 2
7. if you flip a cornﬁ times, how many total outcomes are there? 3. .2— 31 3—  2 Q ” A city soccer league has 7 teams. In how many possible ways could the league assign the ﬁrst and s ' '2 ¥ 1‘  é  "—“
econd place trophies at the end of the season. .1 ”W t 5* 2 , _
9. The Math Club at TCC is made up ofggpeople @nales and®emales Suppose the club eiects
officers for President. Vice President, Secretary, and Treasurer 'nd_t e number of ways t electt
ofﬁcers, if each must be a 93339 22 . 2' ' 3° ' LL: l 5 566 22 {”5" it 22 i3} "“5560 i» W T T
10. A box contains grad balls, 4 white balls, 2 yellow balls, and 1 green ball. in how man; ways can you randomly select 3 white balls and 1 red ball? (4 (23% (3C, ) 2 “P“‘s' :33; trﬁimkl enter NOW???“ 11. Six high school seniors are to be selected from a group of thirty high school seniors. Each of the six will
receive a free ticket to Grad Night tWalt Disney rid—Hewma s can he selection be made.
Prizes the gamejse meter “61' Mtg: ' 30 PH— 6 3o CG: '= 5’93, 37*}; er Bot/(24M!) e 5931'HL5 12. Ten people volunteer to work in a brain bowl competi ion. niy our are needed to work. One would act
as moderator, one would keep score, one would keep time, and one would be a runner. Assuming all ten people could perform all t etasksrb many w oucht assign
may; mgr. {OPICA‘L mm: 5040 re re! 6525040 or 13. Mrs. Brown is giving a bridal shower for a friend. Due to her hectic schedule, she decides to hire a
caterer. The caterer offers Wedges and .12 desserts. Mrs. Brown decides to choose 3 3. 4 (c
appetizers and 2 desserts. How many ways can these selections be made? , ,2; a‘h x K125}
. (O , ‘ .. J: Qibeoién' "\.—"‘" X —* Mk7€f003xczc2i“ xii'7‘," 1' ‘7‘ I
_ V . (3! [D 2
. s can seven childre line u ? 7' ‘ .. 
14 HOW ma 940}! n '12 ‘uf‘fgrLJngcﬁhéL '1‘;ng  :26 K H _ ?‘(_c, of ¥Vi=§eqo or
Answers: 1. 12Q; 2. Counting Principle (CP) —26260260101010 3.15103 or CF ‘ 4. 10C5 7102 or CP 8. CP—9'10010'10026'26 7.CP25 8. 7P2 9. 221194 10, 4C3'3Cr
ii. 39C6 12. 10134 13. 10C3'12C2 14. 7P7OI‘CP CountingIProbabiiity Unit . 6/?
Conditional Probability Handout— Use with 11.7 One hundred students were surveyed and the resutts are recorded in the table below. < — Takin 16 hours kin 7 12 hours akin 1318 hours Ta FAMU 7' ”2100 ~
if one student is seiected at random, ﬁnd the prgtghiiity that heatshe: she /he ' 3m?” 5'93”
E 7 V ng ED 25 ' h (g):
1. lsaFAMUstudent. P(Et>= “(5) 1‘ 15:: I t‘ our “Bhutan 'fb EDI? [if graham") E2 is a FAMU student iven that the are takin 712 hours i? ‘  i
. '93 y 9 ' ( géré:j: {7(FAMHI7ﬂl): %;Q E 3. ts taking ?~12 hours, given that the are a FAMU student. . 
y We) = Petal mu) ”3 (new mm +0 “it
E4. is a IQQ studentéﬁa E§U student. 101 35‘, 25‘ ﬂ 3 FAAE FM“ 3
131.1545: 165 ‘fﬁ‘z‘ E5. is taking 1318 hours, given that they are a TCC student. . 5 _ _t_
E _ 13(55): Wattcc} "2e «
8. Is an FSU student takin 1318 hours.
E P655) :" F’CFSQ and. l3/Isg): i3ﬂoo = Q/EQ
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7 is $33931“ gyisbgﬁen: 2%; arfp§5E§[email protected]%Et%1tb F5“ winch so. a 3 r
E 8. is a student FSU or FAMU or ch. ' L’ (90355 i
’9. is a five ye old student in Mrs. Nash's kindergarten ciass.
£90393 = @ E10. is a mo student, given that theﬁking 712 hours. (st/,2 {m B a calm“;
PCE:¢\ : PCTCCl 7/11) ; ZO/él For each of the following, a single card is drawn from a standard deck of 52. Find the obabiiity that the card:
, 3  33 .2 3.233333:
11. Is a heart, given that it is red. (Veshict‘tﬁﬁtkw, “ls 7390‘ CW PCE" ' 24 26 red ._ J1 :
12. is red, given that it is a heart. P(E.L\ = Pﬁe“ l F’WJ‘) ”" '3 © 3 Pictures '2 statuses 13. Is a picture card, given that it is a club. Pain) [email protected] W cm“;
3 _.
club i new“ : E" g 4 ”kid we 14. is a club, given that it is a picture card. 1905.43 = P( A bag contains each of the numbers 1 — 20, written on separate pieces of paper. One numbeﬂrris selected at 'h—t—_ random. What is the probability that the __ mber chosen is: l0; H) ‘3’) [3215) {51%; 1.1L) L3; ‘9’ 1° ‘
( >— e :9 ’
15. An even number. P 515 '' 20 _ ,6
1 (Mt. LLT>9) : '
16. An even number, given that the number selected is greater than 9. 4905”,) t F (em I M L " _ . 3
17. An 11, given that the number selected is even. P (5:23 5 ‘3 (0” MP5)“ * 5 9
18. A number greater than 9,.that the number selected is odd. P ( Era) ~“ TE 5 my?“ ') 3) 5) 7'5 32.2) £31313, 1: 7/; Using a standard deck of 52 cards, you are to draw two cards' to succession without replacement. Find the Conditional Probability continued fd FObabillty 0 FaWIHQ 3 4 .5qu of? £2 for 1.3—I draw K (Md) ﬁugéﬂdﬁw
19.TwoKing$. 190519)” 3 1! xi— 2. I? ,1 6
20. A two first and a picture card second 4 52) I: H"— X "d" 1—» '= i lg 7 ”L K._' “t.
21 Twos ades .13 P62 0) :@ P(Cao) 52 “ 5! :5 1?
PC (523 51 9' _ ”L . q (215) 12090911"D
x zgggggargfggangggcmd m 95133336111221 P111114 mm
23 The ﬁrst 1.511015% face carda 9 3c 'h’ieﬁ? an“ ““1 9' ”"1"“? I
the ond is not a face card. _§z
’P(Eza> _. 4: x 39 : :0 x, 1% "(1%) 2;; Mcnmf'au: (Md; A BRAIN STRETCHER: DRAW 5 CARDS IN SUCCESSION WITHOUT REPLACEMENT. FIND THE :CJBABILITY OF DRAWING 5 CLUBS.
' I3 12 II {o 9 {31/211 1&9 __ 13R; :@ EXETXZF:W¥?§ ” 52 5150 49.99 ’ 3st w
7 49 9121)  33
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9
.nswers 1.}— 2.1 3.12 4.2 5.} f3.1 7.1 8.1 9.0 10.& 11,1.
4 3 25 4 8 so 35 51 2
12 1 13. i 14.}— 15. i 16. 3 17.0 18. 1 19. "1— 20.1L 21. i
13 4 2 11 2 221 221 17
22. i 23. Q 24. 33 orz0.0005
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