I know the next formula:
$P\left(A\cap B \cap C \right)=P\left( A\right) P\left( B\mid A\right) P\left(C\mid B\cap A\right) $
How could we define the next probabilities?
a) $P\left( A\cap B\mid C\right) $
b) $P\left( A\mid B\cap C\right) $
Thank you this would help me a lot.
Sorry, just figured my own question:
$P\left( A\cap B|C\right) = \dfrac{P\left(A\cap B \cap C \right)}{P\left( C\right) }$
$P\left( A|B\cap C\right) = \dfrac{P\left(A\cap B \cap C \right)}{P\left( B\cap C\right) }$