$P(A,B|C)=P(B|C)P(A|B,C)$
Does this property have a unique name? How do we derive it and what are the properties? Does it come from Bayes only or do we need other properties?
2026-05-04 10:00:56.1777888856
What is this equality called and what are the conditions?
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That is the definition of conditional probability. Everything in the equation is "given $C$." So if we ignore that, it simplifies to $$ P(A,B) = P(B)\cdot P(A|B)$$