Presentation on theme: "Pertemuan 03 Teori Peluang (Probabilitas)"— Presentation transcript:
1 Pertemuan 03 Teori Peluang (Probabilitas) Matakuliah : I0262 – Statistik ProbabilitasTahun : 2007Versi : RevisiPertemuan 03 Teori Peluang (Probabilitas)
2 Mahasiswa akan dapat menjelaskan ruang contoh dan peluang kejadian. Learning OutcomesPada akhir pertemuan ini, diharapkan mahasiswaakan 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 MateriIstilah/ notasi dalam peluangDiagram Venn dan Operasi HimpunanPeluang kejadianKaidah-kaidah peluangPeluang bersyarat, kejadian bebas dan kaidah Bayes
4 Introduction to Probability Experiments, Counting Rules, andAssigning ProbabilitiesEvents and Their ProbabilitySome Basic Relationships of ProbabilityConditional ProbabilityBayes’ Theorem
5 ProbabilityProbability 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 thenumber of experimental outcomes when n objects are tobe selected from a set of N objects.Number of combinations of N objects taken n at a timewhere 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 thenumber of experimental outcomes when n objects are tobe selected from a set of N objects where the order ofselection is important.Number of permutations of N objects taken n at a time
8 Complement of an EventThe 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 SEvent AAc
9 Union of Two EventsThe 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 BThe union of A and B is illustrated below.Sample Space SEvent AEvent 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 SIntersectionEvent AEvent B
11 Addition LawThe 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 EventsP(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 LawThe 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 EventsEvents A and B are independent if P(A|B) = P(A).
16 Independent EventsMultiplication Law for Independent EventsP(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 DiagramP(Bc|A1) = .8P(A1) = .7P(A2) = .3P(B|A2) = .9P(Bc|A2) = .1P(B|A1) = .2P(A1 B) = .14P(A2 B) = .27P(A2 Bc) = .03P(A1 Bc) = .56
18 Bayes’ TheoremTo 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.