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Suppose that events F and S are conditional independent events given D and ~D respectively with p(F|D)=p(S|D)=0.9, p(~F|~D)=p(~S|~D)=0.9, and p(D)=0.2. Find p(D|F∩S).

Respuesta :

P(D|FS)=.9529

If F and S are conditionally independent given D and ~D, then

P(FSD)= P(D)P(F|D)P(S|D)

P(FS~D) = P(~D)P(F|~D)P(S|~D)

P(F|~D) = 1 - P(~F|~D)

P(S|~D) = 1 - P(~S|~D)

P(~D) = 1 - P(D)

P(D|FS) = P(FSD)/(P(FSD) + P(FS~D))

P(F|D) = P(S|D) = .9

P(~F|~D) = P(~S|~D) = .9

P(D = .2)

Then, P(FSD) = P(D)P(F|D)P(S|D) = .2*.9*.9 = .162

P(FS~D) = P(~D)P(F|~D)P(S|~D) = (1 - .2)(1 - .9)(1 - .9)= .008

P(D|FS) = P(FSD)/(P(FSD) + P(FS~D)) = .162/(.162+.008) = 162/170=81/85 = .9529

To learn more about conditional independent events follow link : https://brainly.com/question/12783373

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