1、1Copyright 2019,2015,2012,Pearson Education,Inc.ChapterProbability32Copyright 2019,2015,2012,Pearson Education,Inc.Chapter Outline3.1 Basic Concepts of Probability and Counting3.2 Conditional Probability and the Multiplication Rule3.3 The Addition Rule3.4 Additional Topics in Probability and Countin
2、g3Copyright 2019,2015,2012,Pearson Education,Inc.Section 3.3The Addition Rule.4Copyright 2019,2015,2012,Pearson Education,Inc.Section 3.3 Objectives How to determine whether two events are mutually exclusive How to use the Addition Rule to find the probability of two events.5Copyright 2019,2015,2012
3、,Pearson Education,Inc.Mutually Exclusive EventsMutually exclusive Two events A and B cannot occur at the same time A and B have no outcomes in commonA and B are mutually exclusiveA and B are not mutually exclusive.6Copyright 2019,2015,2012,Pearson Education,Inc.Example:Recognizing Mutually Exclusiv
4、e EventsDetermine whether the events are mutually exclusive.Explain your reasoning.1.Event A:Roll a 3 on a die.Event B:Roll a 4 on a die.Solution:Mutually exclusive(The first event has one outcome,a 3.The second event also has one outcome,a 4.These outcomes cannot occur at the same time.).7Copyright
5、 2019,2015,2012,Pearson Education,Inc.Example:Recognizing Mutually Exclusive EventsDetermine whether the events are mutually exclusive.Explain your reasoning.2.Event A:Randomly select a male student.Event B:Randomly select a nursing major.Solution:Not mutually exclusive(The student can be a male nur
6、sing major.)8Copyright 2019,2015,2012,Pearson Education,Inc.Example:Recognizing Mutually Exclusive EventsDetermine whether the events are mutually exclusive.Explain your reasoning.3.Event A:Randomly select a blood donor with type O blood.Event B:Randomly select a female blood donor.Solution:Not mutu
7、ally exclusive(The donor can be a female with type O blood)9Copyright 2019,2015,2012,Pearson Education,Inc.The Addition RuleAddition rule for the probability of A or B The probability that events A or B will occur is P(A or B)=P(A)+P(B)P(A and B)For mutually exclusive events A and B,the rule can be
8、simplified to P(A or B)=P(A)+P(B)Can be extended to any number of mutually exclusive events.10Copyright 2019,2015,2012,Pearson Education,Inc.Example:Using the Addition Rule to Find Probabilities 1.You select a card from a standard deck.Find the probability that the card is a 4 or an ace.Solution:The
9、 events are mutually exclusive(if the card is a 4,it cannot be an ace)(4)(4)()44525280.15452Por acePP ace.11Copyright 2019,2015,2012,Pearson Education,Inc.Example:Using the Addition Rule to Find Probabilities 2.You roll a die.Find the probability of rolling a number less than 3 or rolling an odd num
10、ber.Solution:The events are not mutually exclusive(1 is an outcome of both events).12Copyright 2019,2015,2012,Pearson Education,Inc.Solution:Using the Addition Rule to Find Probabilities(3)(3)()(3)23140.6676666P less thanor oddP less thanP oddP less thanand odd.13Copyright 2019,2015,2012,Pearson Edu
11、cation,Inc.Example:Finding Probabilities of Mutually Exclusive EventsThe frequency distribution shows volumes of sales(in dollars)and the number of months in which a sales representative reached each sales level during the past three years.Using this sales pattern,find the probability that the sales
12、 representative will sell between$75,000 and$124,999 next month.Sales volume($)Months024,999325,00049,999550,00074,999675,00099,9997100,000124,9999125,000149,9992150,000174,9993175,000199,9991.14Copyright 2019,2015,2012,Pearson Education,Inc.Solution:Finding Probabilities of Mutually Exclusive Event
13、s A=monthly sales between$75,000 and$99,999 B=monthly sales between$100,000 and$124,999 A and B are mutually exclusiveSales volume($)Months024,999325,00049,999550,00074,999675,00099,9997100,000124,9999125,000149,9992150,000174,9993175,000199,9991.15Copyright 2019,2015,2012,Pearson Education,Inc.Solu
14、tion:Finding Probabilities of Mutually Exclusive Events A=monthly sales between$75,000 and$99,999 B=monthly sales between$100,000 and$124,999 A and B are mutually exclusiveSales volume($)Months024,999325,00049,999550,00074,999675,00099,9997100,000124,9999125,000149,9992150,000174,9993175,000199,9991
15、()()()793636160.44436P Aor BP AP B.16Copyright 2019,2015,2012,Pearson Education,Inc.Example:Using the Addition Rule to Find ProbabilitiesA blood bank catalogs the types of blood,including whether it is Rh-positive or Rh-negative,given by donors during the last five days.The number of donors who gave
16、 each blood type is shown in the table.1.Find the probability the donor has type O or type A blood.Type OType AType BType ABTotalRh-Positive1561393712344Rh-Negative 28 25 8 4 65Total1841644516409.17Copyright 2019,2015,2012,Pearson Education,Inc.Solution:Using the Addition Rule to Find ProbabilitiesT
17、he events are mutually exclusive(a donor cannot have type O blood and type A blood)Type OType AType BType ABTotalRh-Positive1561393712344Rh-Negative 28 25 8 4 65Total1841644516409()()()1841644094093480.851409P typeO or type AP typeOP type A.18Copyright 2019,2015,2012,Pearson Education,Inc.Example:Us
18、ing the Addition Rule to Find Probabilities2.Find the probability the donor has type B or is Rh-negative.Solution:The events are not mutually exclusive(a donor can have type B blood and be Rh-negative)Type OType AType BType ABTotalRh-Positive1561393712344Rh-Negative 28 25 8 4 65Total1841644516409.19
19、Copyright 2019,2015,2012,Pearson Education,Inc.Solution:Using the Addition Rule to Find ProbabilitiesType OType AType BType ABTotalRh-Positive1561393712344Rh-Negative 28 25 8 4 65Total1841644516409()()()()456581020.249409409409409P type B or RhnegP type BP RhnegP type B and Rhneg.20Copyright 2019,20
20、15,2012,Pearson Education,Inc.A Summary of Probability21Copyright 2019,2015,2012,Pearson Education,Inc.Example:Combining Rules to Find ProbabilitiesUse the figure to find the probability that a randomly selected draft pick is not a running back or a wide receiver.22Copyright 2019,2015,2012,Pearson Education,Inc.Solution:Combining Rules to Find Probabilities23Copyright 2019,2015,2012,Pearson Education,Inc.Solution:Combining Rules to Find Probabilities
