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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)