Matakuliah
Tahun
Versi
: A0064 / Statistik Ekonomi
: 2005
: 1/1
Pertemuan 5
Probabilitas-1
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Menjelaskan pengertian, aturan-aturan
dasar, jenis,kondisi, dan manfaat
probabilitas, pengertian dan kebebasan
suatu kejadian, ruang sampel dan konsep
kombinasi
2
Outline Materi
• Pengertian dasar kejadian, ruang sampel,
dan probabilitas
• Aturan-aturan Dasar Probabilitas
• Kebebasan Suatu Kejadian
• Konsep-konsep Kombinasi
3
COMPLETE
BUSINESS STATISTICS
2-4
5th edi tion
Probability
2
Using Statistics
 Basic Definitions: Events, Sample Space, and
Probabilities
 Basic Rules for Probability
 Conditional Probability
 Independence of Events
 Combinatorial Concepts
 The Law of Total Probability and Bayes’ Theorem
 Summary and Review of Terms

McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-5
5th edi tion
2-1 Probability is:




A quantitative measure of uncertainty
A measure of the strength of belief in the
occurrence of an uncertain event
A measure of the degree of chance or
likelihood of occurrence of an uncertain
event
Measured by a number between 0 and 1 (or
between 0% and 100%)
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-6
5th edi tion
Types of Probability

Objective or Classical Probability
based on equally-likely events
based on long-run relative frequency of events
not based on personal beliefs
 is the same for all observers (objective)
examples: toss a coin, throw a die, pick a card
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-7
5th edi tion
Types of Probability (Continued)

Subjective Probability
based on personal beliefs, experiences,
prejudices, intuition - personal judgment
different for all observers (subjective)
examples: Super Bowl, elections, new product
introduction, snowfall
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-8
5th edi tion
2-2 Basic Definitions

Set - a collection of elements or objects of
interest
Empty set (denoted by )

a set containing no elements
Universal set (denoted by S)

a set containing all possible elements

a set containing all elements of S not in A
Complement (Not). The complement of A is  A 
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-9
5th edi tion
Complement of a Set
S
A
A
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-10
5th edi tion
Basic Definitions (Continued)
Intersection (And)  A  B
–
a set containing all elements in both A and B
Union (Or)  A  B
–
McGraw-Hill/Irwin
a set containing all elements in A or B or
both
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
2-11
BUSINESS STATISTICS
5th edi tion
Sets: A Intersecting with B
S
A
B
A B
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
2-12
BUSINESS STATISTICS
5th edi tion
Sets: A Union B
S
A
B
A B
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-13
5th edi tion
Basic Definitions (Continued)
• Mutually exclusive or disjoint sets
–sets having no elements in common, having
no intersection, whose intersection is the
empty set
• Partition
–a collection of mutually exclusive sets which
together include all possible elements, whose
union is the universal set
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-14
5th edi tion
Mutually Exclusive or Disjoint Sets
Sets have nothing in common
S
A
McGraw-Hill/Irwin
Aczel/Sounderpandian
B
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
2-15
BUSINESS STATISTICS
5th edi tion
Sets: Partition
S
A3
A1
A2
A4
A5
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
2-16
BUSINESS STATISTICS
5th edi tion
Experiment
•
Process that leads to one of several possible
outcomes *, e.g.:
 Coin toss
• Heads,Tails
 Throw die
• 1, 2, 3, 4, 5, 6
 Pick a card
• AH, KH, QH, ...
•
•
Introduce a new product
Each trial of an experiment has a single observed
outcome.
The precise outcome of a random experiment is
unknown before a trial.
* Also called a basic outcome, elementary event, or simple event
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-17
5th edi tion
Events : Definition

Sample Space or Event Set
 Set of all possible outcomes (universal set) for a given
experiment

E.g.: Throw die
– S = {1,2,3,4,5,6}

Event
 Collection of outcomes having a common characteristic

E.g.: Even number
– A = {2,4,6}
– Event A occurs if an outcome in the set A occurs

Probability of an event
 Sum of the probabilities of the outcomes of which it
consists

McGraw-Hill/Irwin
P(A) = P(2) + P(4) + P(6)
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-18
5th edi tion
Equally-likely Probabilities
(Hypothetical or Ideal Experiments)
•
For example:
 Throw a die
• Six possible outcomes {1,2,3,4,5,6}
• If each is equally-likely, the probability of each is 1/6 = .1667
= 16.67%
1
P
(
e
)

•
n( S )
• Probability of each equally-likely outcome is 1 over the
number of possible outcomes
 Event A (even number)
• P(A) = P(2) + P(4) + P(6) = 1/6 + 1/6 + 1/6 = 1/2
• P( A)   P( e) for e in A
n( A ) 3 1

 
n( S ) 6 2
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
2-19
BUSINESS STATISTICS
5th edi tion
Pick a Card: Sample Space
Union of
Events ‘Heart’
and ‘Ace’
P ( Heart  Ace ) 
n ( Heart  Ace )

n(S )
16
4

52
13
Hearts
Diamonds
Clubs
A
K
Q
J
10
9
8
7
6
5
4
3
2
A
K
Q
J
10
9
8
7
6
5
4
3
2
A
K
Q
J
10
9
8
7
6
5
4
3
2
Event ‘Heart’
n ( Heart )
P ( Heart ) 
13

n(S )
1

52
Spades
A
K
Q
J
10
9
8
7
6
5
4
3
2
Event ‘Ace’
n ( Ace )
P ( Ace ) 
n(S )
4
52
13
n ( Heart  Ace )
1

n(S )
Aczel/Sounderpandian
1

The intersection of the
events ‘Heart’ and ‘Ace’
comprises the single point
circled twice: the ace of hearts
P ( Heart  Ace ) 
McGraw-Hill/Irwin
4

52
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-20
5th edi tion
2-3 Basic Rules for Probability

Range of Values 0  P( A) 1

Complements - Probability of not A
P( A )  1  P( A)

Intersection - Probability of both A and B
P( A  B)  n( A  B)
n( S )
 Mutually exclusive events (A and C) :
P( A  C )  0
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-21
5th edi tion
Basic Rules for Probability (Continued)
•
Union - Probability of A or B or both (rule of unions)
P( A  B)  n( A  B)  P( A)  P( B)  P( A  B)
n( S )
 Mutually exclusive events: If A and B are mutually exclusive, then
P( A  B)  0 so P( A  B)  P( A)  P( B)
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
2-22
BUSINESS STATISTICS
5th edi tion
Sets: P(A Union B)
S
A
B
P( A  B)
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
COMPLETE
BUSINESS STATISTICS
2-23
5th edi tion
Basic Rules for Probability (Continued)
•
Conditional Probability - Probability of A given B
P( A B) 
P( A  B)
, where P( B)  0
P( B)
 Independent events:
P( A B)  P( A)
P( B A)  P( B)
McGraw-Hill/Irwin
Aczel/Sounderpandian
© The McGraw-Hill Companies, Inc., 2002
Penutup
• Pembahasan dilanjutkan dengan Materi
Pokok-6 (Probabilitas-2)
24