Solved – it $frac{P(Acap Bcap C)}{P(Bcap C)}$

(My question is prompted by this post.)

I'm not understanding why $frac{P(Acap Bcap C)}{P(Bcap C)}$is not equal to $frac{P(A)P(B)P(C)}{P(B)P(C)} = P(A)$. I know it's wrong but I cannot understand why. Can you explain it please?

If $A$, $B$, and $C$ are mutually independent you can say $P(Acap Bcap C)= P(A)P(B)P(C)$. But, in general case, they are not independent, and you can't always say that.

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