Presentation on theme: "Pertemuan 03 Peluang Kejadian"— Presentation transcript:
1 Pertemuan 03 Peluang Kejadian Matakuliah : A Statistik EkonomiTahun : 2006Pertemuan 03 Peluang Kejadian
2 Outline Materi:Konsep dasar peluangPeluang bebas dan bersyaratPeluang total dan kaidah Bayes
3 Basic Business Statistics (9th Edition) Basic Probability
4 Basic Probability Concepts Konsep Dasar PeluangBasic Probability ConceptsSample spaces and events, simple probability, joint probabilityConditional ProbabilityStatistical independence, marginal probabilityBayes’ TheoremCounting Rules
5 Collection of All Possible Outcomes Sample SpacesCollection of All Possible OutcomesE.g., All 6 faces of a die:E.g., All 52 cards of a bridge deck:
6 Kejadian (Events) Simple Event Joint Event Outcome from a sample space with 1 characteristicE.g., a Red Card from a deck of cardsJoint EventInvolves 2 outcomes simultaneouslyE.g., an Ace which is also a Red Card from a deck of cards
7 Visualizing Events Contingency Tables Tree Diagrams Black 2 24 26 Ace Not Ace TotalBlackRedTotalAceRedCardsNot an AceFullDeckof CardsAceBlackCardsNot an Ace
8 A Deck of 52 Cards Contingency Table Red Ace Total Ace Red 2 24 26 Not anAceTotalAceRed22426Black22426Total44852Sample Space
9 Event Possibilities Tree Diagram Ace Red Cards Not an Ace Full Deck of CardsAceBlackCardsNot an Ace
10 ProbabilityProbability is the Numerical Measure of the Likelihood that an Event Will OccurValue is between 0 and 1Sum of the Probabilities of All Mutually Exclusive and Collective Exhaustive Events is 11Certain.5Impossible
11 Computing Probabilities The Probability of an Event E:Each of the Outcomes in the Sample Space is Equally Likely to OccurE.g., P( ) = 2/36(There are 2 ways to get one 6 and the other 4)
12 Computing Joint Probability The Probability of a Joint Event, A and B:
13 Joint Probability Using Contingency Table EventEventB1B2TotalA1P(A1 and B1)P(A1 and B2)P(A1)A2P(A2 and B1)P(A2 and B2)P(A2)TotalP(B1)P(B2)1Marginal (Simple) ProbabilityJoint Probability
14 Computing Compound Probability Probability of a Compound Event, A or B:
15 Compound Probability (Addition Rule) P(A1 or B1 ) = P(A1) + P(B1) - P(A1 and B1)EventEventB1B2TotalA1P(A1 and B1)P(A1 and B2)P(A1)A2P(A2 and B1)P(A2 and B2)P(A2)TotalP(B1)P(B2)1For Mutually Exclusive Events: P(A or B) = P(A) + P(B)
16 Computing Conditional Probability The Probability of Event A Given that Event B Has Occurred:
17 Conditional Probability Using Contingency Table ColorTypeRedBlackTotalAce224Non-Ace242448Total262652Revised Sample Space
18 Conditional Probability and Statistical Independence Multiplication Rule:
19 Conditional Probability and Statistical Independence Events A and B are Independent ifEvents A and B are Independent When the Probability of One Event, A, is Not Affected by Another Event, B(continued)
20 Adding up the parts of A in all the B’s Bayes’ TheoremAdding up the parts of A in all the B’sSame Event
21 Bayes’ Theorem Using Contingency Table 50% of borrowers repaid their loans. Out of those who repaid, 40% had a college degree. 10% of those who defaulted had a college degree. What is the probability that a randomly selected borrower who has a college degree will repay the loan?
22 Bayes’ Theorem Using Contingency Table (continued)RepayRepayTotalCollege.2.05.25.3.45.75CollegeTotal.5.51.0
23 Counting Rule 1If any one of k different mutually exclusive and collectively exhaustive events can occur on each of the n trials, the number of possible outcomes is equal to kn.E.g., A six-sided die is rolled 5 times, the number of possible outcomes is 65 = 7776.
24 Counting Rule 2If there are k1 events on the first trial, k2 events on the second trial, …, and kn events on the n th trial, then the number of possible outcomes is (k1)(k2)•••(kn).E.g., There are 3 choices of beverages and 2 choices of burgers. The total possible ways to choose a beverage and a burger are (3)(2) = 6.
25 Counting Rule 3The number of ways that n objects can be arranged in order is n! = n (n - 1)•••(1).n! is called n factorial0! is 1E.g., The number of ways that 4 students can be lined up is 4! = (4)(3)(2)(1)=24.
26 Counting Rule 4: Permutations The number of ways of arranging X objects selected from n objects in order isThe order is important.E.g., The number of different ways that 5 music chairs can be occupied by 6 children are
27 Counting Rule 5: Combintations The number of ways of selecting X objects out of n objects, irrespective of order, is equal toThe order is irrelevant.E.g., The number of ways that 5 children can be selected from a group of 6 is