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)