Conditional Probability on the Intersection Property

313 Views Asked by At

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.

1

There are 1 best solutions below

0
On

Sorry, just figured my own question:

$P\left( A\cap B|C\right) = \dfrac{P\left(A\cap B \cap C \right)}{P\left( C\right) }$

$P\left( A|B\cap C\right) = \dfrac{P\left(A\cap B \cap C \right)}{P\left( B\cap C\right) }$