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I have five independent events $E_1,E_2,E_3,E_4, E_5$, with their conditional probability values for a given outcome.

Eg - $P(Y|E_1), P(Y|E_2), P(Y|E_3), P(Y|E_4), P(Y|E_5)$

Given the above can I find $P(Y|E_1, E_2), P(Y|E_4, E_3, E_5)$? which is basically any combination of the above events given as the condition. It does not have to be exact even an approximation is sufficient.

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No.   You need much more information about the series of $\{E_k\}$ events and their relation to $Y$.

For instant, since we have the following, we can see that we cannot express $\mathsf P(Y\mid E_1, E_2)$ in terms of $\mathsf P(Y\mid E_1),\mathsf P(Y\mid E_2)$ with just the given details.

$$\mathsf P(Y\mid E_1, E_2) =\frac{\mathsf P(Y, E_1\mid E_2)}{\mathsf P(E_1\mid E_2)} = \frac{\mathsf P(Y, E_1, E_2)}{\mathsf P(E_1, E_2)}$$

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  • $\begingroup$ Thank you for the answer, can you please tell me what other type of information I would need. $\endgroup$ – himani Nov 23 '15 at 0:36
  • $\begingroup$ @himani Obviously information sufficient to find or simplify the numerator and denominator of at least one of the quotients. $\endgroup$ – Graham Kemp Nov 23 '15 at 0:40
  • $\begingroup$ If I have values for example P(Y|E1, E2), P(Y|E2, E3), P(Y|E3,E1). Can I find the value of P(Y|E1,E2,E3) will this be an acceptable approximation? $\endgroup$ – himani Nov 23 '15 at 0:43

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