Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-1,Business Statistics: A Decision-Making Approach 6th Edition,Chapter 4 Using Probability and Probability Distributions,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-2,Chapter Goals,After completing this chapter, you should be able to: Explain three approaches to assessing probabilities Apply common rules of probability Use Bayes Theorem for conditional probabilities Distinguish between discrete and continuous probability distributions Compute the expected value and standard deviation for a discrete probability distribution,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-3,Important Terms,Probability the chance that an uncertain event will occur (always between 0 and 1) Experiment a process of obtaining outcomes for uncertain events Elementary Event the most basic outcome possible from a simple experiment Sample Space the collection of all possible elementary outcomes,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-4,Sample Space,The Sample Space is the collection of all possible outcomes e.g. All 6 faces of a die:e.g. All 52 cards of a bridge deck:,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-5,Events,Elementary event An outcome from a sample space with one characteristicExample: A red card from a deck of cards Event May involve two or more outcomes simultaneouslyExample: An ace that is also red from a deck ofcards,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-6,Visualizing Events,Contingency TablesTree Diagrams,Red 2 24 26,Black 2 24 26,Total 4 48 52,Ace Not Ace Total,Full Deck of 52 Cards,Red Card,Black Card,Not an Ace,Ace,Ace,Not an Ace,Sample Space,Sample Space,2 24 2 24,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-7,Elementary Events,A automobile consultant records fuel type and vehicle type for a sample of vehicles2 Fuel types: Gasoline, Diesel3 Vehicle types: Truck, Car, SUV6 possible elementary events:e1 Gasoline, Trucke2 Gasoline, Care3 Gasoline, SUVe4 Diesel, Trucke5 Diesel, Care6 Diesel, SUV,Gasoline,Diesel,Car,Truck,Truck,Car,SUV,SUV,e1 e2 e3 e4 e5 e6,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-8,Probability Concepts,Mutually Exclusive Events If E1 occurs, then E2 cannot occur E1 and E2 have no common elements,Black Cards,Red Cards,A card cannot be Black and Red at the same time.,E1,E2,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-9,Independent and Dependent Events Independent: Occurrence of one does not influence the probability of occurrence of the otherDependent: Occurrence of one affects the probability of the other,Probability Concepts,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-10,Independent EventsE1 = heads on one flip of fair coinE2 = heads on second flip of same coin Result of second flip does not depend on the result of the first flip. Dependent EventsE1 = rain forecasted on the newsE2 = take umbrella to work Probability of the second event is affected by the occurrence of the first event,Independent vs. Dependent Events,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-11,Assigning Probability,Classical Probability Assessment,Relative Frequency of Occurrence,Subjective Probability Assessment,P(Ei) =,Number of ways Ei can occur Total number of elementary events,Relative Freq. of Ei =,Number of times Ei occurs N,An opinion or judgment by a decision maker about the likelihood of an event,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-12,Rules of Probability,Rules for Possible Values and Sum,Individual Values,Sum of All Values,0 P(ei) 1 For any event ei,where:k = Number of elementary events in the sample spaceei = ith elementary event,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-13,Addition Rule for Elementary Events,The probability of an event Ei is equal to the sum of the probabilities of the elementary events forming Ei. That is, if: Ei = e1, e2, e3then: P(Ei) = P(e1) + P(e2) + P(e3),Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-14,Complement Rule,The complement of an event E is the collection of all possible elementary events not contained in event E. The complement of event E is represented by E.Complement Rule:,E,E,Or,Business Statistics: A Decision-Making Approach, 6e 2005 Prentice-Hall, Inc.,Chap 4-15,Addition Rule for Two Events,