M ARIO F . T RIOLA
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1 Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman MARIO F. TRIOLA EIGHTH EDITION ELEMENTARY STATISTICS Section 3-3 Addition Rule
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S TATISTICS. E LEMENTARY. Section 3-3 Addition Rule. M ARIO F . T RIOLA. E IGHTH. E DITION. Compound Event Any event combining 2 or more simple events. Definition. Compound Event Any event combining 2 or more simple events Notation - PowerPoint PPT Presentation
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1Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
MARIO F. TRIOLAMARIO F. TRIOLA EIGHTHEIGHTH
EDITIONEDITION
ELEMENTARY STATISTICS Section 3-3 Addition Rule
2Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Compound Event Any event combining 2 or more simple events
Definition
3Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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
4Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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
5Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Formal Addition RuleP(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
6Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Formal Addition RuleP(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 RuleTo 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
7Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
DefinitionEvents A and B are mutually exclusive if they
cannot occur simultaneously.
8Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
DefinitionEvents 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
9Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
DefinitionEvents A and B are mutually exclusive if they
cannot occur simultaneously.
Figures 3-5 and 3-6
Total Area = 1 Total Area = 1
P(A) P(B) P(A) P(B)
P(A and B)
Non-overlapping EventsOverlapping Events
10Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Figure 3-7 Applying the Addition Rule
P(A or B)
Addition Rule
AreA and Bmutuallyexclusive
?
P(A or B) = P(A)+ P(B) - P(A and B)
P(A or B) = P(A) + P(B)Yes
No
11Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Find the probability of randomly selecting a man or a boy.
Men Women Boys Girls Totals
Survived 332 318 29 27 706
Died 1360 104 35 18 1517
Total 1692 422 64 56 2223
Contingency Table
12Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Find the probability of randomly selecting a man or a boy.
Men Women Boys Girls Totals
Survived 332 318 29 27 706
Died 1360 104 35 18 1517
Total 1692 422 64 56 2223
Contingency Table
13Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Find the probability of randomly selecting a man or a boy.
P(man or boy) = 1692 + 64 = 1756 = 0.7902223 2223 2223
Men Women Boys Girls Totals
Survived 332 318 29 27 706
Died 1360 104 35 18 1517
Total 1692 422 64 56 2223
Contingency Table
14Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Find the probability of randomly selecting a man or a boy.
P(man or boy) = 1692 + 64 = 1756 = 0.7902223 2223 2223
Men Women Boys Girls Totals
Survived 332 318 29 27 706
Died 1360 104 35 18 1517
Total 1692 422 64 56 2223
Contingency Table
* Mutually Exclusive *
15Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Find the probability of randomly selecting a man or someone who survived.
Men Women Boys Girls Totals
Survived 332 318 29 27 706
Died 1360 104 35 18 1517
Total 1692 422 64 56 2223
Contingency Table
16Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Find the probability of randomly selecting a man or someone who survived.
Men Women Boys Girls Totals
Survived 332 318 29 27 706
Died 1360 104 35 18 1517
Total 1692 422 64 56 2223
Contingency Table
17Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Find the probability of randomly selecting a man or someone who survived.
P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223
Men Women Boys Girls Totals
Survived 332 318 29 27 706
Died 1360 104 35 18 1517
Total 1692 422 64 56 2223
Contingency Table
= 0.929
18Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Find the probability of randomly selecting a man or someone who survived.
P(man or survivor) = 1692 + 706 - 332 = 1756 2223 2223 2223 2223
Men Women Boys Girls Totals
Survived 332 318 29 27 706
Died 1360 104 35 18 1517
Total 1692 422 64 56 2223
Contingency Table
* NOT Mutually Exclusive *
= 0.929
19Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Complementary Events
P(A) and P(A)are
mutually exclusive
20Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Complementary Events
P(A) and P(A)are
mutually exclusive
All simple events are either in A or A.
21Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. 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
22Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Rules of Complementary Events
P(A) + P(A) = 1
23Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
P(A)
Rules of Complementary Events
P(A) + P(A) = 1
= 1 - P(A)
24Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
P(A) + P(A) = 1
= 1 - P(A)
P(A) = 1 - P(A)
P(A)
Rules of Complementary Events
25Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Figure 3-8 Venn Diagram for the Complement of Event A
Total Area = 1
P (A)
P (A) = 1 - P (A)
