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.


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.

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

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.