Probability >Probability is the numerical Certain measure of the likelihood that an event will occur >Value is between 0 and 1 .5 >Sum of the probabilities of all mutually exclusive and collectively exhaustive events is 1 Impossible Statistics for Ma agers Using Microsoft Excel Chap 4-11 Tongji University,School of Economics Management
Statistics for Managers Using Microsoft Excel Chap 4-11 Tongji University, School of Economics & Management Probability Probability is the numerical measure of the likelihood that an event will occur Value is between 0 and 1 Sum of the probabilities of all mutually exclusive and collectively exhaustive events is 1 Certain Impossible .5 1 0
Computing Probabilities >The probability of an event E: number of event outcomes P(E)= total number of possible outcomes in the sample space For example,the probability of drawing an ace from a standard deck of cards is:P(Ace)=4/52 >Each of the outcomes in the sample space is equally likely to occur Statistics fo agers Using Microsoft Excel Chap 4-12 Tongji University,School of Economics Management
Statistics for Managers Using Microsoft Excel Chap 4-12 Tongji University, School of Economics & Management Computing Probabilities The probability of an event E: Each of the outcomes in the sample space is equally likely to occur number of event outcomes ( ) total number of possible outcomes in the sample space P E X T For example, the probability of drawing an ace from a standard deck of cards is: P(Ace) = 4/52
Computing Joint Probability >The probability of a joint event,A and B: P(4 and B)=P(A∩B) number of outcomes from both A and B total number of possible outcomes in sample space If we draw a card from a standard deck or cards,what is the probability it will be a red ace(red and ace)? E.g.P(Red Card and Ace) 2 Red Aces 52 Total Number of Cards 26 Statistics for Ma agers Using Microsoft Excel Chap 4-13 Tongji University,School of Economics Management
Statistics for Managers Using Microsoft Excel Chap 4-13 Tongji University, School of Economics & Management Computing Joint Probability The probability of a joint event, A and B: ( and ) = ( ) number of outcomes from both A and B total number of possible outcomes in sample space P A B PA B E.g. (Red Card and Ace) 2 Red Aces 1 52 Total Number of Cards 26 P If we draw a card from a standard deck or cards, what is the probability it will be a red ace (red and ace)?
Joint Probability Using Contingency Table Event Event BI B2 Total Al P(A:and B) P(A and B2) P(Ap) A P(A2 and B) P(A2 and B2) P(A2) Total P(B) P(B2) Joint Probability Marginal (Simple)Probability Statistics for Managers Using Microsoft Excel Chap4-14 Tongji University,School of Economics Management
Statistics for Managers Using Microsoft Excel Chap 4-14 Tongji University, School of Economics & Management P(A1 and B2) P(A1) Event Total Joint Probability Using Contingency Table P(A2 and B1) P(A1 and B1) Event Total 1 Joint Probability Marginal (Simple) Probability A1 A2 B1 B2 P(B1) P(B2) P(A2 and B2) P(A2)