7-3-2 - 7-3 Part II Independent EventsExperiment flip a...

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Unformatted text preview: 7-3 Part II: Independent EventsExperiment: flip a coin twice•P(event A = two heads = HH) = 1/4•but 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 ½ “•written as: P(A | B) = 1/2•note: P(A) ≠P(A | B)•the information I have given you about the occurrence of event B changes P(A) from ¼ to ½ •when the known occurrence of one event changesthe probability of occurrence of another, we say that the two events are not independent•do the experiment again; now•A = head on 2ndflip , B = head on 1stflip•P(A) = ½ •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(A∩B)/P(B) = (1/4)/(1/2) = ½ •answer: no -- P(A | B) = P(A)for two events, ifthe unconditional probability = the conditional probabilitywe say the events are independent7-3 Part IIp. 1•now,...
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7-3-2 - 7-3 Part II Independent EventsExperiment flip a...

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