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S TATISTICS. E LEMENTARY. Section 3-4 Multiplication Rule: Basics. M ARIO F . T RIOLA. E IGHTH. E DITION. Finding the Probability of Two or More Selections. Multiple selections Multiplication Rule. Notation. P(A and B) = P(event A occurs in a first trial and - PowerPoint PPT Presentation
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1Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
MARIO F. TRIOLAMARIO F. TRIOLA EIGHTHEIGHTH
EDITIONEDITION
ELEMENTARY STATISTICS Section 3-4 Multiplication Rule: Basics
2Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Finding the Probability of Two or More Selections
Multiple selections
Multiplication Rule
3Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
NotationP(A and B) =
P(event A occurs in a first trial and
event B occurs in a second trial)
4Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
TaTbTcTdTeFaFbFcFdFe
a
b
c
d
e
a
b
c
d
e
T
F
FIGURE 3-9 Tree Diagram of Test Answers
5Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
TaTbTcTdTeFaFbFcFdFe
a
b
c
d
e
a
b
c
d
e
T
F
FIGURE 3-9 Tree Diagram of Test Answers
6Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
TaTbTcTdTeFaFbFcFdFe
a
b
c
d
e
a
b
c
d
e
T
F
P(T) =
FIGURE 3-9 Tree Diagram of Test Answers
12
7Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
TaTbTcTdTeFaFbFcFdFe
a
b
c
d
e
a
b
c
d
e
T
F
P(T) = P(c) =
FIGURE 3-9 Tree Diagram of Test Answers
12
15
8Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
TaTbTcTdTeFaFbFcFdFe
a
b
c
d
e
a
b
c
d
e
T
F
P(T) = P(c) = P(T and c) =
FIGURE 3-9 Tree Diagram of Test Answers
12
15
110
9Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
P (both correct)
10Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
P (both correct) = P (T and c)
11Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
P (both correct) = P (T and c)
1 10
1 2
1 5
12Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
P (both correct) = P (T and c)
1 10
1 2
1 5
= •
MultiplicationRule
13Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
P (both correct) = P (T and c)
1 10
1 2
1 5
= •
MultiplicationRule
INDEPENDENT EVENTS
14Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
P(B A) represents the probability of event B occurring after it is assumed that event A has already occurred (read B A as “B given A”).
Notation for Conditional Probability
15Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Definitions
Independent EventsTwo events A and B are independent if the occurrence of one does not affect the probability of the occurrence of the other.
Dependent EventsIf A and B are not independent, they are said to be dependent.
16Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Formal Multiplication Rule
P(A and B) = P(A) • P(B A)
If A and B are independent events, P(B A) is really the same as P(B)
17Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Figure 3-10 Applying the Multiplication Rule
P(A or B)
Multiplication Rule
AreA and B
independent?
P(A and B) = P(A) • P(B A)
P(A and B) = P(A) • P(B)Yes
No
18Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Intuitive Multiplication
When finding the probability that event A occurs in one trial and B occurs in the next trial, multiply the probability of event A by the probability of event B, but be sure that the probability of event B takes into account the previous occurrence of event A.
19Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
Small Samples from
Large Populations
If a sample size is no more than 5% of the size of the population, treat the selections as being independent (even if the selections are made without replacement, so they are technically dependent).
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