《统计学基础(英文版·第7版)》教学课件les7e03 03.pptx

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1、Chapter,Probability,3,Chapter Outline,3.1 Basic Concepts of Probability and Counting3.2 Conditional Probability and the Multiplication Rule3.3 The Addition Rule3.4 Additional Topics in Probability and Counting,Section 3.3,The Addition Rule,.,Section 3.3 Objectives,How to determine whether two events

2、 are mutually exclusiveHow to use the Addition Rule to find the probability of two events,.,Mutually Exclusive Events,Mutually exclusiveTwo events A and B cannot occur at the same timeA and B have no outcomes in common,A and B are mutually exclusive,A and B are not mutually exclusive,.,Example: Reco

3、gnizing 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 oc

4、cur 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 (The student can be a male nursing m

5、ajor.),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 (The donor can be a female with

6、type O blood),The Addition Rule,Addition rule for the probability of A or BThe probability that events A or B will occur isP(A or B) = P(A) + P(B) P(A and B)For mutually exclusive events A and B, the rule can be simplified toP(A or B) = P(A) + P(B)Can be extended to any number of mutually exclusive

7、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,Y

8、ou 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 fr

9、equency 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.,.,So

10、lution: Finding Probabilities of Mutually Exclusive Events,A = monthly sales between $75,000 and $99,999B = monthly sales between $100,000 and $124,999A and B are mutually exclusive,.,Solution: Finding Probabilities of Mutually Exclusive Events,A = monthly sales between $75,000 and $99,999B = monthl

11、y sales between $100,000 and $124,999A and B are mutually exclusive,.,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 blo

12、od type is shown in the table. Find the probability the donor has type O or type A blood.,.,Solution: Using the Addition Rule to Find Probabilities,The events are mutually exclusive (a donor cannot have type O blood and type A blood),.,Example: Using the Addition Rule to Find Probabilities,Find the

13、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),.,Solution: Using the Addition Rule to Find Probabilities,.,A Summary of Probability,Example: Combining Rules to Find Probabilities,Use the figure to

14、find the probability that a randomly selected draft pick is not a running back or a wide receiver.,Solution: Combining Rules to Find Probabilities,Solution:Define events A and B.A: Draft pick is a running back.B: Draft pick is a wide receiver.These events are mutually exclusive, so the probability t

15、hat the draft pick is a running back or wide receiver isP(A or B) = P(A) + P(B) = 23 253 + 31 253 = 54 253 .,Solution: Combining Rules to Find Probabilities,Solution:By taking the complement of P(A or B), you can determine that the probability of randomly selecting a draft pick who is not a running back or wide receiver is1 P(A or B) = 1 54 253 = 199 253 0.787.,