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I have a simple question: what is the difference, if at all, between

$$ P(A|X,Y) $$


$$ P(A|X\And Y) $$

and what form would these two take if represented using bayes theorem? thanks

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up vote 4 down vote accepted

If $A$, $X$ and $Y$ are events then I would read them as being the same.

You have $$\Pr(A|X,Y) = \dfrac{\Pr(X,Y|A)\Pr(A)}{\Pr(X,Y)}$$ (assuming the denominator is positive) which you can also write many different ways, such as $$\Pr(A|X,Y) = \dfrac{\Pr(X|A,Y)\Pr(Y|A)\Pr(A)}{\Pr(X|Y)\Pr(Y)}.$$

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