1、统计学基础(英文版第7版)教学课件les7e_ppt_03_03Chapter Outline 3.1 Basic Concepts of Probability and Counting 3.2 Conditional Probability and the Multiplication Rule 3.3 The Addition Rule 3.4 Additional Topics in Probability and CountingSection 3.3The Addition Rule.Section 3.3 Objectives How to determine whether t
2、wo events are mutually exclusive How to use the Addition Rule to find the probability of two events.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.Example:
3、Recognizing Mutually Exclusive 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
4、at the same time.).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 nursing major.)Example
5、: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 mutually exclusive(The donor can be a female with type O blood)The Addi
6、tion 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 simplified to P(A or B)=P(A)+P(B)Can be extended to any number of mutually exclusive events.Example:Using the Addit
7、ion 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 events are mutually exclusive(if the card is a 4,it cannot be an ace)(4)(4)()44525280.15452Por acePP ace.Example:Using the Addition Rule to Find Probabilities 2.Yo
8、u roll a die.Find the probability of rolling a number less than 3 or rolling an odd number.Solution:The events are not mutually exclusive(1 is an outcome of both events).Solution:Using the Addition Rule to Find Probabilities(3)(3)()(3)23140.6676666P less thanor oddP less thanP oddP less thanand odd.
9、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 representa
10、tive 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.Solution:Finding Probabilities of Mutually Exclusive Events A=monthly sales between$75,000 and$99,999 B=monthly sales
11、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.Solution:Finding Probabilities of Mutually Exclusive Events A=monthly sales between$75,000 and$99,999 B=monthly s
12、ales 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()()()793636160.44436P Aor BP AP B.Example:Using the Addition Rule to Find ProbabilitiesA blood bank catalogs
13、 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 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-Ne
14、gative 28 25 8 4 65Total1841644516409.Solution:Using the Addition Rule to Find ProbabilitiesThe 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()()()1841644094093480.85140
15、9P typeO or type AP typeOP type A.Example:Using 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-Positive1561393712344R
16、h-Negative 28 25 8 4 65Total1841644516409.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.A Summary of ProbabilityExample: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.Solution:Combining Rules to Find ProbabilitiesSolution:Combining Rules to Find Probabilities
