Event B student participated in a prep class Did prep class increase chance of

Event b student participated in a prep class did prep

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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 eventProbability 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) > 0Posterior Probability– a revision of the prior probability using additional informationConditional Probabilities in BusinessHow probable for customer with credit card balance less than $3,000 to pay entire balance in any given monthProbability that a 40-year-old female customer will choose to purchase anextended warranty form the factoryIndependent and Dependent EventsIndependent– two events are independent of one another if the occurrence of one event has no impact on the occurrence of the other eventEx:-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)
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Dependent– two events are dependent when the occurrence of one event affects the occurrence of another eventEx:-Event A = you earn an A grade on your exam-Event B = you study many hours preparing for your examEvent B has impact on Event A in example aboveStep by StepEx: Deb wins tennis matches more when she has a longer warm-upWARMUP TIMEShortLongTOTALDefine the events of interest-Event A = Deb wins-Event B = the warm-up time is longFind 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) = 0.7How to determine whether dependent OR independent events-If independent, P(A|B) = P(A)The Multiplication RuleMultiplication 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 dependentThe 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
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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 contentAs first bag is removed, reduces sample space (to 31) for second selection-P(A and B) = probability that both bags will be low on saltFinding 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 saltThe Formula: Multiplication Rule for 2 Independent EventsP(A and B) = P(A) • P(B)
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