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STATISTICS
Chapter 5b Probability Addition Rule
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Compound Event Any event combining 2 or more simple events
Definition
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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
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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
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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
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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
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DefinitionEvents A and B are mutually exclusive if they
cannot occur simultaneously.
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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
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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
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Figure 5-7 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
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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
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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
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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
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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 *
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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
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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
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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
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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
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Complementary Events
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Complementary Events
P(A) and P(A)are
mutually exclusive
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Complementary Events
P(A) and P(A)are
mutually exclusive
All simple events are either in A or A.
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Complementary Events
P(A) and P(A)are
mutually exclusive
All simple events are either in A or A.
P(A) + P(A) = 1
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Rules of Complementary Events
P(A) + P(A) = 1
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P(A)
Rules of Complementary Events
P(A) + P(A) = 1
= 1 - P(A)
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P(A) + P(A) = 1
= 1 - P(A)
P(A) = 1 - P(A)
P(A)
Rules of Complementary Events
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Figure 5-8 Venn Diagram for the Complement of Event A
Total Area = 1
P (A)
P (A) = 1 - P (A)