ELEMENTARY
STATISTICS
Section 3-4
Multiplication Rule: Basics
EIGHTH
EDITION
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
MARIO F. TRIOLA
1
Finding the Probability of Two
or More Selections
 Multiple selections
 Multiplication Rule
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
2
Notation
P(A and B) =
P(event A occurs in a first trial and
event B occurs in a second trial)
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
3
FIGURE 3-9
Tree Diagram of Test Answers
T
F
a
b
c
d
e
a
b
c
d
e
Ta
Tb
Tc
Td
Te
Fa
Fb
Fc
Fd
Fe
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
4
FIGURE 3-9
Tree Diagram of Test Answers
T
F
a
b
c
d
e
a
b
c
d
e
Ta
Tb
Tc
Td
Te
Fa
Fb
Fc
Fd
Fe
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
5
FIGURE 3-9
Tree Diagram of Test Answers
T
F
P(T) =
a
b
c
d
e
a
b
c
d
e
Ta
Tb
Tc
Td
Te
Fa
Fb
Fc
Fd
Fe
1
2
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
6
FIGURE 3-9
Tree Diagram of Test Answers
T
F
P(T) =
1
2
Ta
Tb
Tc
Td
Te
Fa
Fb
Fc
Fd
Fe
a
b
c
d
e
a
b
c
d
e
P(c) =
1
5
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
7
FIGURE 3-9
Tree Diagram of Test Answers
T
F
P(T) =
1
2
Ta
Tb
Tc
Td
Te
Fa
Fb
Fc
Fd
Fe
a
b
c
d
e
a
b
c
d
e
P(c) =
1
5
1
P(T and c) = 10
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
8
P (both correct)
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
9
P (both correct) = P (T and c)
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
10
P (both correct) = P (T and c)
1
10
1
2
1
5
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
11
P (both correct) = P (T and c)
1 =
10
1
1
•
2
5
Multiplication
Rule
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
12
P (both correct) = P (T and c)
1 =
10
1
1
•
2
5
Multiplication
Rule
INDEPENDENT EVENTS
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
13
Notation for
Conditional Probability
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”).
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
14
Definitions
 Independent Events
Two events A and B are independent if the
occurrence of one does not affect the
probability of the occurrence of the other.
 Dependent Events
If A and B are not independent, they are
said to be dependent.
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
15
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)
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
16
Figure 3-10
Applying the Multiplication Rule
P(A or B)
Multiplication Rule
Are
A and B
independent
?
Yes
P(A and B) = P(A) • P(B)
No
P(A and B) = P(A) • P(B A)
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
17
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.
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
18
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).
Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman
19