I NO (HM'HJSL; Basic l'iolia'aiiity C H ""Tx P 'i CHECi'iNG YO ' Ui? UNDERST 4.38 What are the ditferenc AND'NG ' .. es rc . . empirical probability between a pl'lOl'l probabilitv. and subjective ' ' 7 ' probabil t '2 4.39 What is the difference l y joint event? between a simple event and a 4.40 How can you use the probability of occurrence 0 general addition mle to find the f event A or B? 4.41 Wl ' ' events anziat is the difference between mutually exclllSiVe collectively exhaustive events? 4.42 HOW dOe . . . S conditional ' ' cept O f m dependence? probability relate to the con- 4.43 ' ' ' How does the multiplication rule differ for events that are and are not independent? 4.4 , How can you use Bayes theorem to revise probabili- ties m light of new information? 4.45 In Bayes' theorem, how does the prior probability dif- fer from the revised probability? APPLYlNG THE CONCEPTS 4.46 A survey by the Pew Research Center ("Snapshotsz Goals of 'Gen Next' vs. 'Gen X,'" USA Today, March 27, 2007, p. lA) indicated that 81% of 18- to 25-year-olds had getting rich as a goal, as compared to 62% of 26- to 40-year- olds. Suppose that the survey was based on 500 respondents from each of the two groups. a. Form a contingency table. b. Give an example of a simple event and a joint event. c. What is the probability that a randomly selected respon- dent has a goal of getting rich? What is the probability that a randomly selected respon- dent has a goal of getting rich and is in the 26- to 40- year-old group? et Are the events "age group" and "has getting rich as a goal" independent? Explain. d. 4.47 The owner of a restaurant serving Continental-style entres was interested in studying ordering patterns of patrons for the Friday-to-Sunday weekend time period. Records were maintained that indicated the demand for dessert during the same time period. The owner decided to study two other variables, along with whether a dessert was ordered: the gender of the individual and whether a beef entre was ordered. The results are as follows: GENDER DESSERT ORDERED Male Female Total Yes 96 40 l 36 No get an 4.265 Total 320 280 600 as; REViEW westerns BEEF E . ESSERY QBERED noted that Yes statement NO H GSXXEY ideas. 0; Tutal T; Mg ' ' acmely d 7 X' extracted ( IC A waiter approaches a table to take an is the probability that the first enstomorderfOr tilt sum 3. orders a dessert? er '0 urducr serene" u b. orders a dessert or haS ordered a beef , 4.50 S] c. is a female and does not order enira gmerall . a dessert") s VT)- d. is a female or does not order a deSSe q. n i 'l 0. Suppose the first person from whomr; isis V. dessert order is a female. What is the e wait/gm ' 5 does not order dessert? probabilirp, imam f. Are gender and ordering dessert independ A. Wii g. Is ordering a beef entre independent of am? Tesr." son orders dessert? "het: Consic 4.48 James Choi, DaVid Laibson, and Brigitte Mat. ducted an experiment to study the ch "" selection. Suppose 100 undergraduate Student; at. ' s< MBA students were selected..Wheri presented 500 Index funds that were identical exceptfmfi.' b CC undergraduate and MBA students chose the firms; am an smart" (is R FUND U xx 4.51 ndergmfim ' most Lowest-cost fund 19 Viru: Second-lowest-cost fund 37 "Yu Third-lowest-eost fund 17 deg! Highest-cost fund 27 gm UP Source: Data extracted from J. J. Choi, D. Laibson, ME C '-'. virt Why Does the Law of One Price Fail: An Experiment with! l any www.som.yale.eduIfaculty/jjcSS/fees.pdf. pos the If a student is selected at random, what isthet'y' the that he or she yi fm a. selected the lowest- or second-lowest-costiul- b. selected the lowest-cost fund and is an "WE: TE c. selected the lowest-cost fund or is an Ti d. Given that a student is an undergraduaieij'; Ca probability that he or she selected the hiihdtiji T' gilv' e. Do you think undergraduate students a dents differ in their fund selection? Expla' ' fl . '5 iii" 4.49 According to a Gallup Poll, compagm; ees who are engaged with their workplace las vation, productivity, and profitabiliiY' ME; 4 employee turnover. A survey of 1.793 "'0 Mr" a found that 13% of the workers were engage Wa engaged, and 20% were actively discntlage '