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