if X and Y are events which are independent of each other, but neither are independent with A,(adsbygoogle = window.adsbygoogle || []).push({});

is this equality true for conditional probabilities:

P( X, Y | A) = P(X|A) * P(Y|A)

if not,

how do you solve for P(A | X,Y)

given that you only know P (A) and P(X|A) and P(Y|A)?

The reason I came up with the above probability where I have:

[tex] P(A| X, Y) = \frac {P(X, Y | A) P(A)}{P(X, Y |A) P(A) + P(X, Y | A^c) P (A^c)} [/tex]

is that I used Baye's Thm.

Note: P(X, Y |A) is not given.

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# Homework Help: Independence and conditional probability

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