- #1
island-boy
- 99
- 0
if X and Y are events which are independent of each other, but neither are independent with A,
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.
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.