Conditional probability given two dependent events

Question

Given A and a couple of events $E_{1}$ and $E_{2}$ (that we now are mutually dependent) we want to compute:

$P(A|E_1, E_2)$

Is there a way to compute this? What would I need? Most of the solutions I have found assume independence of $E_{1}$ and $E_{2}$.

Answer 1

Basically you need $\mathsf P(A,E_1,E_2)$ and $\mathsf P(E_1,E_2)$, some way to get them, or a similar pair of probability measures.$$\mathsf P(A\mid E_1,E_2)=\dfrac{\mathsf P(A,E_1,E_2)}{\mathsf P(E_1,E_2)}=\dfrac{\mathsf P(A,E_1\mid E_2)}{\mathsf P(E_1\mid E_2)}=\textit{et. cetera}$$