Event B = student participated in a prep class-Did prep class increase chance of high score?■Probability of Event A-P(A) = 42/250 or 0.168 (16.8%)-Prior probability– the probability of Event A occurring as determined w/o any additional information that could influence the event■Probability of P(A|B)-Event A, given that Event B has already occurred-Sample space reduced to Event B (70 students)-22 of 70 from prep class scored in 601-800-22/70 = 0.314 = P(A|B)○Formula for calculating a conditional probabilityP(A|B) = P(A and B) ¸ P(B) Where P(B) > 0 ORP(B|A) = P(A and B) ¸ P(A)Where P(A) > 0○Posterior Probability– a revision of the prior probability using additional information○Conditional Probabilities in Business■How probable for customer with credit card balance less than $3,000 to pay entire balance in any given month■Probability that a 40-year-old female customer will choose to purchase anextended warranty form the factory●Independent and Dependent Events○Independent– two events are independent of one another if the occurrence of one event has no impact on the occurrence of the other event■Ex:-Event A = today I purchased the next iPhone-Event B = later in day, Apple announces cool new features of next iPhone (which I don’t have)

○Dependent– two events are dependent when the occurrence of one event affects the occurrence of another event■Ex:-Event A = you earn an A grade on your exam-Event B = you study many hours preparing for your exam■Event B has impact on Event A in example above○Step by Step■Ex: Deb wins tennis matches more when she has a longer warm-upWARMUP TIMEShortLongTOTAL■Define the events of interest-Event A = Deb wins-Event B = the warm-up time is long■Find marginal probability of Event A-11/25 (Deb wins match) = 0.44 or 44%■Find conditional probability of P(A|B)-P(A|B) = P(A and B) ¸ P(B)-P(A and B) = 7/25 (0.28)-P(B) = 10/25 (0.4)-(0.28) ¸ (0.4) = 0.7■How to determine whether dependent OR independent events-If independent, P(A|B) = P(A)●The Multiplication Rule○Multiplication Rule– used to determine the probability of the intersection (joint probability) of two events occurring, or P(A and B).■Assumes that Events A and B are dependent○The Formula: Multiplication Rule for Dependent EventsP(A|B) = P(A and B) ¸ P(B)P(A and B) = P(B) • P(A|B)ORP(B|A) = P(A and B) ¸ P(A) P(A and B) = P(A) • P(B|A)○Example: Salty Potato Chips

32 bags on shelf, 9 contain low salt content, probability that both bags (2) you select will have low salt content?■Define the Events-Event A = the first bag selected will have low salt content-Event B = the 2ndbag selected will have low salt content■As first bag is removed, reduces sample space (to 31) for second selection-P(A and B) = probability that both bags will be low on salt■Finding Probability-P(A) = 9/32 (0.281)-P(B|A) = 8/31 (0.258)■Multiplication Rule-P(A and B) = (0.281) • (0.258) = 0.072-à 7% chance both bags selected will be low salt○The Formula: Multiplication Rule for 2 Independent EventsP(A and B) = P(A) • P(B)■

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- Fall '12
- Donnelly
- Standard Deviation, Mean