MGF 1106 ‐ Review of probability #2   Determine sample space and probabilities for various experiments.  A.  Tossing coins ‐ Three coins are to be tossed. 

MGF 1106 ‐ Review of probability #2 Determine sample space and probabilities for various experiments. A. Tossing coins ‐ Three coins are to be tossed. 1. Use the fundamental counting principle to determine the total number of possible outcomes. 2. Make a tree diagram and list the sample space. 3. Determine each of the following probabilities. P(three heads) = P(at least one head) = P(at least two heads) = P(exactly two heads| first toss is heads) = P(at least one heads| first toss is tails) = P(heads then tails then heads) = B. Filling offices ‐ Larry, Moe and Curly plan to form a club with each member holding one of the following offices: president, vice‐president and treasurer. 1. Use the fundamental counting principle to determine the number of ways the offices can be filled. 2. Make a tree diagram and list the sample space. 3. Determine each of the following probabilities: P(Larry is president and Moe is vice‐president) = P(Curly is treasurer) = P(Moe is president) = P(Moe is vice‐president or Curly is president) = P(Moe is vice‐president and Curly is president) = C. Drawing cards ‐ 1. One card is to be drawn from a standard card deck. P(Ace of hearts) = P(Ace or King) = P(Black face card) = P(even number) = P(Ace or black card) = P(Ace of spades| the card is black) = 2. Two cards are to be drawn with replacement. P(Ace and king) = P(Ace and Ace) = P(Ace and not Ace) = P(club and spade) = 3. Two cards are to be drawn without replacement. P(Ace and king) = P(Ace and Ace) = P(Ace and not Ace) = P(club and spade) = D. From a chart ‐ 1. Results of a recent survey are as follows: Yes No No opinion Total Republican 20 12 12 44 Democrat 25 8 5 38 Independent 6 5 7 18 Total 51 25 24 100 Based on this survey, find the probability of each response. P(yes) = P(no) = P(no| democrat) = P(no opinion| independent) = P(yes or no) = ANSWERS : A. 1. 1/8, 7/8, 1/2, 1/2, 3/4, 1/8 B. 1. 1/6, 1/3, 1/3, 1/2, 1/6 C. 1. 1/52, 8/52=2/13, 6/52=3/26, 20/52=5/13, 28/52=7/13, 1/26 2. 1/169, 1/169, 12/169, 1/16 3. 4/663, 1/221, 16/221, 13/204 D. 1. 51/100, 25/100, 2/19, 7/18, 19/25 ___________________________________________________________________________________________ MGF1106Chapter12Review–PartB
1.Apiggybankcontains3quarters,2dimes,and5nickels.Onecoinisshakenoutandthenputbackin
beforeasecondcoinisshakenout.Whatistheprobabilitythefirstcoinwillbeaquarterandthesecond
coinwillbeadime?
2.Thereare10horsesinaraceandonlythreewinningplaces:win,place,andshow.Howmanypossible
winningarrangementsaretherefortheraceof10horses?
3.Fivemenandsixwomenareeligibletoserveonacommitteerequiringtwomenandtwowomen
members.Howmanydifferentwayscanthiscommitteebeselected?
4.Amen’sclothingstoreisofferingmixandmatchsportjacketsandslacks.Thereare10different
jacketsand15differentslacks.Ifamanbuysoneofeachhowmanydifferentoutfitscouldhepurchase?
5.Sportswriterswereaskedtorankfivefootballteamsfrombesttoworst.Howmanydifferentwayscan
theteamsberelated?
6.Inhowmanywayscan7booksbearrangedonashelf?
7.Tengirlstryoutforaswimteam.Howmanyteamsof6girlscanbechosen?
8.Usingthedatainthetablebelow,determinetheprobabilitythatifanewpresidentisselected,the
presidentwillbeagirlgiventhepresidentmustbeasenior.
Seniors
Juniors
TOTAL
Girl
6
2
8
Boy
4
3
7
Total
10
5
15
9.Five$.29stampsandthree$.20stampsarelooseinanenvelope.Ifapersonpickstwostampswithout
looking(withoutreplacement),whatistheprobabilitythestampsareboth$.20stamps?
10.Whatistheprobabilityapersonwouldrandomlyselectathree,giventhenumberisodd?
11.Howmanywayscanyourearrangethelettersoftheword“Mississippi”?
12.Whatistheprobabilityofrandomlyselectinganodddigitoradigitgreaterthan7?
13.Amultiple‐choicetestquestionhasfourchoices.Whatistheprobabilityofnotguessingthecorrect
answer?
14.If70%ofallcollegestudentsjoinaclub,whatistheprobabilitythatarandomlyselectedcollege
studentdoesnotbelongtoaclub?
15.Howmanydifferentwayscanthelettersoftheword"MIME"bearranged?
16.Howmanydifferentwayscanthelettersoftheword"COUNT"bearranged? 17.Acoinistossedandadieisrolled.
a.Howmanydifferentpossibleoutcomesarethere?b.Listthesamplespace.
18.Usingtheinformationfromproblem#17,whatistheprobabilitythataheadistossedandaneven
numberisrolled?
19–20.Ahatcontainsfourmarbles:1yellow,1brown,1purpleand1orange.
19.Iftwomarblesareselectedwithoutreplacement,howmanypointsareinthesamplespace?
20.Listthesamplespace.
50!
21.Evaluatea)
b)6P2c)6C2
49!
22.Apersoninterestedinbuyingacertainmodelofcarcanbuyitwithorwithouteachofthefollowing
optionaccessories:paddedsteeringwheel,plushCorinthianleather,anti‐theftalarmandtalking
dashboard.Howmanywaysaretheseoptionsavailable?
3
3
3
1
3
3
Answers:1) 2)7203)1504)1505)1206)50407)2108) 9) 10) 11)3465012) 13) 14)0.3
50
5
28
5
5
4
1
15)1216)12017)a)12b)H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T618) 19)1220)YB,YP,YO,BY,BP,BO,OY,OP,
4
OB,PY,PB,PO21)a.50b.30 c.1522)16