1. Pertemuan 03 Teori Peluang (Probabilitas)
Matakuliah : I0262 – Statistik Probabilitas
Tahun : 2007
Versi : Revisi
Pertemuan 03 Teori Peluang (Probabilitas)

2. Mahasiswa akan dapat menjelaskan ruang contoh dan peluang kejadian.
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
Mahasiswa akan dapat menjelaskan ruang contoh dan peluang kejadian.
mahasiswa dapat memberi contoh peluang kejadian bebas, bersyarat dan kaidah Bayes.

3. Istilah/ notasi dalam peluang Diagram Venn dan Operasi Himpunan
Outline Materi
Istilah/ notasi dalam peluang
Diagram Venn dan Operasi Himpunan
Peluang kejadian
Kaidah-kaidah peluang
Peluang bersyarat, kejadian bebas dan kaidah Bayes

4. Introduction to Probability
Experiments, Counting Rules, and
Assigning Probabilities
Events and Their Probability
Some Basic Relationships of Probability
Conditional Probability
Bayes’ Theorem

5. Probability
Probability is a numerical measure of the likelihood that an event will occur.
Probability values are always assigned on a scale from 0 to 1.
A probability near 0 indicates an event is very unlikely to occur.
A probability near 1 indicates an event is almost certain to occur.
A probability of 0.5 indicates the occurrence of the event is just as likely as it is unlikely.

6. Counting Rule for Combinations
Another useful counting rule enables us to count the
number of experimental outcomes when n objects are to
be selected from a set of N objects.
Number of combinations of N objects taken n at a time
where N! = N(N - 1)(N - 2) (2)(1)
n! = n(n - 1)( n - 2) (2)(1)
0! = 1

7. Counting Rule for Permutations
A third useful counting rule enables us to count the
number of experimental outcomes when n objects are to
be selected from a set of N objects where the order of
selection is important.
Number of permutations of N objects taken n at a time

8. Complement of an Event
The complement of event A is defined to be the event consisting of all sample points that are not in A.
The complement of A is denoted by Ac.
The Venn diagram below illustrates the concept of a complement.
Sample Space S
Event A Ac

9. Union of Two Events
The union of events A and B is the event containing all sample points that are in A or B or both.
The union is denoted by A B
The union of A and B is illustrated below.
Sample Space S
Event A
Event B

10. Intersection of Two Events
The intersection of events A and B is the set of all sample points that are in both A and B.
The intersection is denoted by A 
The intersection of A and B is the area of overlap in the illustration below.
Sample Space S
Intersection
Event A
Event B

11. Addition Law
The addition law provides a way to compute the probability of event A, or B, or both A and B occurring.
The law is written as:
P(A B) = P(A) + P(B) - P(A  B

12. Mutually Exclusive Events
Addition Law for Mutually Exclusive Events
P(A B) = P(A) + P(B)

13. Conditional Probability
The probability of an event given that another event has occurred is called a conditional probability.
The conditional probability of A given B is denoted by P(A|B).
A conditional probability is computed as follows:

14. Multiplication Law
The multiplication law provides a way to compute the probability of an intersection of two events.
The law is written as:
P(A  B) = P(B)P(A|B)

15. Independent Events
Events A and B are independent if P(A|B) = P(A).

16. Independent Events
Multiplication Law for Independent Events
P(A  B) = P(A)P(B)
The multiplication law also can be used as a test to see if two events are independent.

17. Contoh Soal: L. S. Clothiers
Tree Diagram
P(Bc|A1) = .8
P(A1) = .7
P(A2) = .3
P(B|A2) = .9
P(Bc|A2) = .1
P(B|A1) = .2
P(A1  B) = .14
P(A2  B) = .27
P(A2  Bc) = .03
P(A1  Bc) = .56

18. Bayes’ Theorem
To find the posterior probability that event Ai will occur given that event B has occurred we apply Bayes’ theorem.
Bayes’ theorem is applicable when the events for which we want to compute posterior probabilities are mutually exclusive and their union is the entire sample space.

19. Selamat Belajar Semoga Sukses.