Binomial Probability Worksheet PDF

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4‐2‐2013.BinomialprobabilityandExpectation   Binomialprobability  o Abinomialexperimenthas_________possibleoutcomes:__________________________  o Arepeatedperformanceofabinomialexperimentisa_____________________________  o Arandomvariablex_______________________________________________________  o Aprobabilitydistributionlistsallpossiblevaluesofa_____________________andtheir  ________________________  o Thesumoftheprobabilitiesinanyprobabilitydistributionisalways________________   Example.Constructthebinomialprobabilitydistributionfortossing5coins.           o BinomialProbabilityFormula n=numberofindependentrepetitionsinaBernoullitrial P=probabilityofsuccessofeachrepetition q=probabilityoffailureofeachrepetition(q=1‐p) x=numberofsuccessesthatoccur n‐x=numberoffailuresthatoccur 

P(x) = nCx  px  qn-x 

    

Example1.Tossacoinfivetimes.Findtheprobabilityofobtainingexactlythreeheads.





Example2.Rolladiesixtimes.Findtheprobabilityofobtainingexactlytwo5s.



Example3.Acoupleplanstohave5children.Findtheprobabilitytheywillhavemorethan threegirls.



Example4.Andrewhasawell‐establishedcareerbattingaverageof.300.IfAndrewbats 10times,findtheprobabilitythathewillgetmorethantwohits.

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            

           



Expectedvalue  o Ifarandomvariablexassumesthevaluesx1,x2,…,xnwithprobabilitiesp1,p2,…,pn,the expectedvalueofxis

 E(x)=____________________________________________ 



Example1.Afamilyplanstohavethreechildren.Findtheexpectednumberof boys.



Example2.Aplayerpays$3toplaythefollowinggame:Threecoinsaretossed. Thegamepays$1ifnoheadsappear,$2ifoneheadcomesup,$3iftwoheads appear,and$4ifthreeheadsappear.Findtheplayer’sexpectednetwinnings.



Example3.HowmuchshouldtheplayerpaytoplaythegameinExample2tohave anevenchanceofrecoveringhis/hermoney(thismakesitafairgame)?

       

         

      



Example4.Inacertainstatelottery,aplayerplaysonedollartoplaytheDaily Numbergame:Theplayerchoosesthreedigitsfrom{0,1,…,9}inaspecificorder (000,001,and012areallowed).Thelotteryoperatorrandomlyselectsthreedigits. Iftheplayer’snumbermatches,theplayerwins$600;otherwisehe/sheloses.Find theexpectednetwinnings.



Example5.Aroulettewheelhas18black,18red,and2whitecompartments.The playerplacesa$1betonblackorred.Iftheplayer’scolorcomesuphe/shewins$2; otherwisetheplayerlosesthebet.Findtheexpectednetwinnings.

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