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Unformatted text preview: 73 Part II: Independent EventsExperiment: flip a coin twiceP(event A = two heads = HH) = 1/4but suppose, before I ask the question, I reveal that the event two alike (B = {HH, TT}) has occurred?you would say the probability of A given Bis written as: P(A  B) = 1/2note: P(A) P(A  B)the information I have given you about the occurrence of event B changes P(A) from to when the known occurrence of one event changesthe probability of occurrence of another, we say that the two events are not independentdo the experiment again; nowA = head on 2ndflip , B = head on 1stflipP(A) = but suppose I tell you that event B happened?would that change P(A) from 1/2 to something else?in other words, is P(A  B) = P(A)?look: P(A  B) = P(AB)/P(B) = (1/4)/(1/2) = answer: no  P(A  B) = P(A)for two events, ifthe unconditional probability = the conditional probabilitywe say the events are independent73 Part IIp. 1now,...
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 Spring '11
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 Probability

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