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Ch 4_Black_A - Business Statistics Fifth Edition Ken Black...

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Unformatted text preview: Business Statistics Fifth Edition Ken Black Chapter 4: Probability Not to be reproduced without the written permission of F8. Alt 4—] 4.1 Introduction to Probability (page 98) 0 Synonyms for probability: , 0 Probability is the language of statistics. 0 “An experiment is a process that produces outcomes.” (page 100) 0 We will only consider random experiments (page 100) 0 Characteristics of random experiments: I Can specify all possible outcomes; and, I An outcome cannot be predicted with certainty. Example: Today’s closing price of a security relative to yesterday. P05511316 Which one will occur? outcomes 0 Probability measures the uncertainty of the outcomes. 0 Chapters 4-6 look at ways of dealing with and modelling uncertainty. Not to be reproduced without the written permission of RB. Alt 4—2 4.2 Methods of Assigning Probabilities o The classical method (page 99) o N is the total number of possible mutually exclusive equally likely outcomes. 0 The probability of an event E equals the ratio of the number of outcomes (nE) pertaining to E to the total number of outcomes (N): P(E) = nE IN Examgle: Roll a fair die one time and observe the up face. P (rolling a 6) = Roll a pair of fair dice and observe the up faces P(both up faces are 6’s) = = { Why? Examgle: Each season, Anand’s new fashion designs are shown to a panel of experts — ten R.H.Smith undergraduates - and each secretly votes thumbs up or down. Here are historical data on the panel’s rankings of 1500 designs and the subsequent market success, measured by sales: Number of Positive Panel Votes Sales 7—1 0 4-6 0—3 Total Very successful(V) 380 140 80 600 Modest successful(M) 180 120 100 Disa ointment 40 40 420 Total 600 300 600 1500 What is the probability that a randomly chosen design will be given 7—10 thumbs up? Not to be reproduced Without the written permission of F .B. Alt 4~3 o The Relative Frequency of Occurrence (page 99) o “. . .the probability of an event is equal to the number of times the event has occurred in the past divided by the total number of opportunities for the event to have occurred.” (page 99) 0 Assume an experiment can be repeated indefinitely under identical conditions. The probability of an event E is the long-run relative frequency with which the event E occurs. P(E) = limit (relative frequency) as number of trials —) oo Examgle: Flipping a coin to find the P(Head) Number of heads Relative Frequency 3 out Of5 05 3 out of 5 2 out of 5, Etc. in each of 5 tosses Not to be reproduced without the written permission of PB. Alt 4-4 0 Subjective Probability 0 “Based on the feelings or insights of the person determining the probability.” 0 A way of assigning subjective probabilities Example: What is the probability that the Colts will play in the Super Bowl in 2013? Suppose you say Event (Colts Will Play in Super Bowl) Event (Pick red head) P(Colts Play in Super Bowl) = P(Pick red bead) = DECIDE DEEDS Are you indifi’erent between wagering on either event? If so, then P(Colts will play in Super Bowl in 2013) = If not, then P(Colts will play in Super Bowl in 2013) i o Regardless of how you assign probabilities, 0 s P(E) s 1 for any event Not to be reproduced without the written permission of F.B. Alt 4-5 o 4.5 Addition Laws 0 Special Law of Addition (page 112) I Let X and Y denote any events in a random experiment. I If X and Y are mutually exclusive events (cannot occur simultaneously), P(X or Y) = P(X) + P(Y) S X Y Venn O O diagram Examgle: Number of Positive Panel Votes Sales 7-10 4—6 0-3 Total Very successful(V) ’ 380 140 80 600 Modest successful(M) 180 120 100 400 ’ ' 40 40 Total 600 300 600 1500 What is the probability that a randomly chosen design will be given “7-10” or “4-6” thumbs up? [3(“7—10” or “4—6”) = Not to be reproduced without the written permission of PB. Alt 4-6 0 General Law of Addition (page 107) P(X or Y) = P(X) + P(Y) — P(X and Y) X and Y has been counted twice so subtract once. Examgle: Number of Positive Panel Votes Sales 7-10 4-6 0-3 Total Very successful(V) 380 140 80 600 Modest successful(M) 180 120 100 ointment D 40 40 420 Total 600 300 600 1500 What is the probability that a randomly chosen design will be given 7-10 thumbs up or be “Very Successful”? P(“Very Successful” or “7—10” ) = Not to be reproduced without the written permission of F.B. Alt 4—7 ...
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