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knowing how to use probability

knowing how to use probability

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  • 1. 1ProbabilityPar 9.7 page 699Information 7 March 2013– Check Edulink for memos and MORE INFOon “Counting Principles” & “Probability”.– No official lecture on Tuesday 12 March.Reading work from X-Kit, Chapter 1, 2 & 3.– Tutorial on Wednesday 13 March at 14:40 forrevision (attendance not compulsory).– No homework task or class test next week.– Semester Test on Thursday 14 March.What you should learn …How to find the probabilities of:• Simple events.• Mutually exclusive events.• Independent events & “NotIndependent” events.• Complement of an event.Theory (sample space, events, union, intersection,mutually exclusive, complement, independent)3You should be able to …• Solve theory questions on probability.• List possibilities as Sets.• Solve questions working with VennDiagrams.• Solve questions working with TreeDiagrams.• Solve questions working with Two-wayContingency Tables.4Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 5JJJBKQAJA  BIf A and B are events, their UNION, written A  B, is the event “A or B”consisting of all outcomes in A or in B or in both A and B.A  B = {J, J, J, J, Q, K }Example: A card is drawn at random from a standarddeck of 52 cards.A: getting a club face card B: getting a jack.List the outcomes for the event of getting a club face card orgetting a jack.Example: Union of Two EventsCopyright © by Brooks/Cole, Cengage Learning. All rights reserved. 6If A and B are events, their INTERSECTION, written A  B, is theevent “A and B” consisting of all outcomes common to both A and B.Example: A card is drawn at random from a standard deck of 52cards.A  B = {J}A: getting a club face cardList the outcomes for the event of getting a club face card andgetting a jack.B: getting a jack.JKQAJJJBA  BExample: Intersection of TwoEvents
  • 2. 2Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 7BProbabilityof Union of Two Events).()()()( BAPBPAPBAP If A and B are events, the probability of “A or B” is:A– n(A  B)+ +A  B= ( + ) + ( + ) –n(A  B) = n(A) + n(B)Copyright © by Brooks/Cole, Cengage Learning. All rights reserved. 8Probabilityof Union of Mutually Exclusive Events).()()( BPAPBAP If A and B are MUTUALLY EXCLUSIVE, thenA Bn(A  B)+A and B are mutually exclusiveA  B = 0= n(A) + n(B)= +Independent Events /“Not” Independent EventsIndependent Events: where the outcome of thesecond event is not affected by the outcome ofthe first, “WITH REPLACEMENT”.Not independent events: where the outcome ofthe second event is affected by the outcome ofthe first, “WITHOUT REPLACEMENT”.9ExampleThere are 5 white balls and 3 yellow balls in abox. Select 2 balls in succession from a boxwith replacement and then withoutreplacement. Determine the probability ofselecting:1. 2 yellow balls.2. 1 white and 1 yellow ball.3. At least 1 white ball.10ExampleThe Ace, King and Queen of Diamonds aredrawn from a pack of playing cards and arenot replaced. Determine the probability ofdrawing:1. Another Ace.2. Another Diamond.3. The Ace of Spades.4. A card greater than 10.11Grading of public schools by 1011 adults ina survey1. Calculate the numberof adults who gavepublic schools a B.2. What is the probabilitythat the adult will givethe public schools anA?3. What is the probabilitythe adult will give thepublic schools a C or aD?12
  • 3. 3ExampleAn investigation into sports participation cricket (C) ,Soccer(S) and Volleyball (V) of 240 students at a school yielded thefollowing information:• 13 disabled students cannot participate in any of the sports.• 40 participated in all three sports.• 67 participated in Volleyball (V), but not Cricket (C) orSoccer (S).• 77 participated in Soccer and Volleyball.• 51 participated in Cricket and Soccer.• 154 participated in Volleyball and 120 in Soccer.13Questions1. Draw a Venn-Diagram to illustrate theabove information (let the number that playCricket only be x).2. Show that 30 students play cricket only.3. How many students do not play Soccer?4. What is the probability that a student chosenat random does not play Cricket or Soccer?14Two-Way Table: A travel agent did asurvey amongst his clients as to which typeof holiday they prefer.GameReserveSea Travel TotalMale 450 100 X 700Female 150 150 75 XTotal 600 X X X15Questions1. Complete the two-way table.EVENT A: a person is maleEVENT B: a person prefers a game reserveholiday.2. Are events A and B mutually exclusive?Explain your answer.3. Are events A and B independent? Showthe necessary calculations.16Questions4. If a person is selected at random what isthe probability that the person:• Is not male and prefers traveling holidays.• Prefers game reserve or sea holidays.• Is female or prefers sea holidays?17ExampleIn a game of Lotto 4 numbers are drawn from10 numbers. In how many ways can this bedone if:1. The draw takes place without replacementand where the ordering is important.2. The draw takes place without replacementand where the ordering is not important?3. The draw takes place with replacement?18
  • 4. 4Example19