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 EventAny 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

3Chapter 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

4Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Definition

Events A and B are mutually exclusive

if they cannot occur simultaneously.

5Chapter 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

6Chapter 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

7Chapter 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

8Chapter 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 TotalsSurvived 332 318 29 27 706Died 1360 104 35 18 1517Total 1692 422 64 45 2223

Contingency Table

9Chapter 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 TotalsSurvived 332 318 29 27 706Died 1360 104 35 18 1517Total 1692 422 64 45 2223

Contingency Table

10Chapter 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 TotalsSurvived 332 318 29 27 706Died 1360 104 35 18 1517Total 1692 422 64 45 2223

Contingency Table

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.

P(man or boy) = 1692 + 64 = 1756 = 0.7902223 2223 2223

Men Women Boys Girls TotalsSurvived 332 318 29 27 706Died 1360 104 35 18 1517Total 1692 422 64 45 2223

Contingency Table

* Mutually Exclusive *

12Chapter 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 TotalsSurvived 332 318 29 27 706Died 1360 104 35 18 1517Total 1692 422 64 45 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 someone who survived.

Men Women Boys Girls TotalsSurvived 332 318 29 27 706Died 1360 104 35 18 1517Total 1692 422 64 45 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 someone who survived.

P(man or survivor) = 1692 + 706 - 332 = 2066 2223 2223 2223 2223

Men Women Boys Girls TotalsSurvived 332 318 29 27 706Died 1360 104 35 18 1517Total 1692 422 64 45 2223

Contingency Table

= 0.929

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.

P(man or survivor) = 1692 + 706 - 332 = 2066 2223 2223 2223 2223

Men Women Boys Girls TotalsSurvived 332 318 29 27 706Died 1360 104 35 18 1517Total 1692 422 64 45 2223

Contingency Table

* NOT Mutually Exclusive *

= 0.929

16Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Complementary Events

P(A) and P(A)are

mutually exclusiveAll simple events are either in A or A.

P(A) + P(A) = 1

17Chapter 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

18Chapter 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)

19Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Examples

1) A restaurant has 3 pieces of apple pie, 5 pieces of cherry and 4 pieces of pumpkin pie in its dessert case. If a customer selects a piece of pie what is the probability that it is cherry or pumpkin?

Events are mutually exclusive

P(Cherry or Pumpkin) = P(Cherry) + P(Pumpkin) = 5/12 + 4/12 = 9/12 = 3/4.

20Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Examples

1) A single card is selected from a standard deck of cards. What is the probability that it is a king or club?

Events are not mutually exclusive

P(King or Club) = P(King) + P(Club) – P(King and Club) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13.

21Chapter 3. Section 3-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman

Assignment

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