Stat 321 – Day 4RemindersExample 3: More MatchingExcel?Example 1: Monty Hall ProblemDefinition: ProbabilityAssigning ProbabilitiesSolution to Monty Hall ProblemExample 2: Grad School AdmissionsSlide 10Slide 11Slide 12Slide 13P(AB) vs. P(A'B')For TuesdayStat 321 – Day 4Probability (2.1)RemindersLab 2 due FridayWill discuss similar issues in lectureAsk questions in class/office hours/emailHW 1 due TuesdayCan download data from webCh. 1 questions?Example 3: More MatchingHeightsNumber of siblingsLast haircut costChange in pocketsGuesses of my age1 2345Excel?Column1Mean 22.20533Standard Error 1.213832Median 20.855Mode #N/AStandard Deviation 6.648431Sample Variance 44.20163Kurtosis 5.085073Skewness 1.85294Range 32.75Minimum 13.71Maximum 46.46Sum 666.16Count 30Example 1: Monty Hall ProblemDefinition: ProbabilityWe will consider the probability of an outcome to be the long-run proportion (relative frequency) of times the outcome occurs if the experiment is repeated over and over under identical conditions.Determining probabilitiesSimulationExact analysis…Assigning ProbabilitiesTwo rules:For any event A, P(A) > 0P(S) = 1Thus, 0 < P(A) < 1 for any event ASolution to Monty Hall ProblemReveal Door 1Reveal Door 2Reveal Door 3Total$, pig, pigpig, $, pigpig, pig, $Total 90030030030000000300300150150P(win if staying) = 300/900P(win if switching) = 600/900Example 2: Grad School AdmissionsSuppose that you have applied to two graduate schools, A and B. You believe that the probability of getting accepted by A is .8, by B is .4, and the probability of being rejected by at least one is .65. (a) What is the probability of getting accepted by at least one of the schools?Example 2: Grad School AdmissionsAccepted by ADenied by ATotalAccepted by BDenied by BTotalExample 2: Grad School AdmissionsAccepted by ADenied by ATotalAccepted by B400Denied by B600Total 800 200 1000Example 2: Grad School AdmissionsAccepted by ADenied by ATotalAccepted by B350 400Denied by B600Total 800 200 1000Example 2: Grad School AdmissionsAccepted by ADenied by ATotalAccepted by B350 50 400Denied by B450 150 600Total 800 200 1000P(accepted by A or B (or both)) = 850/1000 = .85BAP(AB) vs. P(A'B')BAFor TuesdayHW 1 dueContinue with Lab 2Any questions so