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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 $E_{2}$.

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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.$$\mathsf P(A\mid E_1,E_2)=\dfrac{\mathsf P(A,E_1,E_2)}{\mathsf P(E_1,E_2)}=\dfrac{\mathsf P(A,E_1\mid E_2)}{\mathsf P(E_1\mid E_2)}=\textit{et. cetera}$$

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  • $\begingroup$ And, assuming a third dependent event $E_{3}$, how would the formula change? $\endgroup$
    – Rors
    Feb 15, 2018 at 12:26
  • $\begingroup$ The obvious way. Add $, E_3$ to the relevant lists. @Rors $\endgroup$
    – Graham Kemp
    Feb 15, 2018 at 12:29
  • $\begingroup$ Really clear, thank you! $\endgroup$
    – Rors
    Feb 15, 2018 at 16:21

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