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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,#,Copyright 2019,2015,2012,Pearson Education,Inc.,Chapter,Probability,3,Chapter 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 Counting,Section 3.3,The Addition Rule,.,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,.,Mutually Exclusive Events,Mutually exclusive,Two events,A,and,B,cannot occur at the same time,A,and,B,have no outcomes in common,A,and,B,are mutually,exclusive,A,and,B,are not mutually exclusive,.,Example:Recognizing Mutually Exclusive Events,Determine whether the events are mutually exclusive.Explain your reasoning.,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.),.,Example:Recognizing Mutually Exclusive Events,Determine whether the events are mutually exclusive.Explain your reasoning.,Event,A,:Randomly select a male student.,Event,B,:Randomly select a nursing major.,.,Solution:,Not mutually exclusive,(T,he student can be a male nursing major.),Example:Recognizing Mutually Exclusive Events,Determine whether the events are mutually exclusive.Explain your reasoning.,Event,A,:Randomly select a blood donor with type O blood.Event,B,:Randomly select a female blood donor.,.,.,Solution:,Not mutually exclusive,(T,he donor can be a female with type O blood,),The Addition Rule,Addition 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 Addition Rule to Find Probabilities,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),.,Example:Using the Addition Rule to Find Probabilities,You 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,.,Example:Finding Probabilities of Mutually Exclusive Events,The 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 representative will sell between$75,000 and$124,999 next month.,Sales volume,($),Months,024,999,3,25,00049,999,5,50,00074,999,6,75,00099,999,7,100,000124,999,9,125,000149,999,2,150,000174,999,3,175,000199,999,1,.,Solution:Finding Probabilities of Mutually Exclusive Events,A,=monthly sales between$75,000 and$99,999,B,=monthly sales between$100,000 and$124,999,A,and,B,are mutually exclusive,Sales volume,($),Months,024,999,3,25,00049,999,5,50,00074,999,6,75,00099,999,7,100,000124,999,9,125,000149,999,2,150,000174,999,3,175,000199,999,1,.,Solution:Finding Probabilities of Mutually Exclusive Events,A,=monthly sales between$75,000 and$99,999,B,=monthly sales between$100,000 and$124,999,A,and,B,are mutually exclusive,Sales volume,($),Months,024,999,3,25,00049,999,5,50,00074,999,6,75,00099,999,7,100,000124,999,9,125,000149,999,2,150,000174,999,3,175,000199,999,1,.,Example:Using the Addition Rule to Find Probabilities,A 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 each blood type is shown in the table.,Find the probability the donor has type O or type A blood.,Type,O,Type A,Type,B,Type AB,Total,Rh-Positive,156,139,37,12,344,Rh-Negative,28,25,8,4,65,Total,184,164,45,16,409,.,Solution:Using the Addition Rule to Find Probabilities,The events are mutually exclusive(a donor cannot have type O blood and type A blood),Type,O,Type A,Type,B,Type AB,Total,Rh-Positive,156,139,37,12,344,Rh-Negative,28,25,8,4,65,Total,184,164,45,16,409,.,Example:Using the Addition Rule to Find Probabilities,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,O,Type A,Type,B,Type AB,Total,Rh-Positive,156,139,37,12,344,Rh-Negative,28,25,8,4,65,Total,184,164,45,16,409,.,Solution:Using the Addition Rule to Find Probabilities,Type,O,Type A,Type,B,Type AB,Total,Rh-Positive,156,139,37,12,344,Rh-Negative,28,25,8,4,65,Total,184,164,45,16,409,.,A Summary of Probability,Example:Combining Rules to Find Probabilities,Use the figure to find the probability that a randomly selected draf
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