1 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 3-3 Addition Rule

2 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman  Compound Event Any event combining 2 or more simple events Definition

3 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman  Compound Event Any event combining 2 or more simple events  Notation P(A or B) = P (event A occurs or event B occurs or they both occur) Definition

4 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman General Rule When finding the probability that event A occurs or event B occurs, find the total number of ways A can occur and the number of ways B can occur, but find the total in such a way that no outcome is counted more than once. Compound Event

5 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Formal Addition Rule P(A or B) = P(A) + P(B) - P(A and B) where P(A and B) denotes the probability that A and B both occur at the same time. Compound Event

6 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Formal Addition Rule P(A or B) = P(A) + P(B) - P(A and B) where P(A and B) denotes the probability that A and B both occur at the same time. Intuitive Addition Rule To find P(A or B), find the sum of the number of ways event A can occur and the number of ways event B can occur, adding in such a way that every outcome is counted only once. P(A or B) is equal to that sum, divided by the total number of outcomes. Compound Event

7 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Definition Events A and B are mutually exclusive if they cannot occur simultaneously.

8 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Definition Events A and B are mutually exclusive if they cannot occur simultaneously. Figures 3-5 Total Area = 1 P(A) P(B) P(A and B) Overlapping Events

9 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Definition Events A and B are mutually exclusive if they cannot occur simultaneously. Figures 3-5 and 3-6 Total Area = 1 P(A) P(B) P(A and B) Non-overlapping Events Overlapping Events

10 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Figure 3-7 Applying the Addition Rule P(A or B) Addition Rule Are A and B mutually exclusive ? P(A or B) = P(A)+ P(B) - P(A and B) P(A or B) = P(A) + P(B) Yes No

11 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Find the probability of randomly selecting a man or a boy. Men Women Boys Girls Totals Survived Died Total Contingency Table

12 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Find the probability of randomly selecting a man or a boy. Men Women Boys Girls Totals Survived Died Total Contingency Table

13 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Find the probability of randomly selecting a man or a boy. P(man or boy) = = 1756 = Men Women Boys Girls Totals Survived Died Total Contingency Table

14 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Find the probability of randomly selecting a man or a boy. P(man or boy) = = 1756 = Men Women Boys Girls Totals Survived Died Total Contingency Table * Mutually Exclusive *

15 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Find the probability of randomly selecting a man or someone who survived. Men Women Boys Girls Totals Survived Died Total Contingency Table

16 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Find the probability of randomly selecting a man or someone who survived. Men Women Boys Girls Totals Survived Died Total Contingency Table

17 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = = Men Women Boys Girls Totals Survived Died Total Contingency Table = 0.929

18 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Find the probability of randomly selecting a man or someone who survived. P(man or survivor) = = Men Women Boys Girls Totals Survived Died Total Contingency Table * NOT Mutually Exclusive * = 0.929

19 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Complementary Events P(A) and P(A) are mutually exclusive

20 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Complementary Events P(A) and P(A) are mutually exclusive All simple events are either in A or A.

21 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Complementary Events P(A) and P(A) are mutually exclusive All simple events are either in A or A. P(A) + P(A) = 1

22 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Rules of Complementary Events P(A) + P(A) = 1

23 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman P(A) Rules of Complementary Events P(A) + P(A) = 1 = 1 - P(A)

24 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman P(A) + P(A) = 1 = 1 - P(A) P(A) = 1 - P(A) P(A) Rules of Complementary Events

25 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman Figure 3-8 Venn Diagram for the Complement of Event A Total Area = 1 P (A) P (A) = 1 - P (A)