Is there anyway, to compute the probability of the event given two dependent events? I know that Bayes can help if those events are independent, but what if condition events are dependent?
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1$\begingroup$ google.co.in/… See if this answer is of help to you. $\endgroup$ – VishwaV Sep 24 '18 at 12:25
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$\begingroup$ Bayes is also called Naive-bayes because treats dependent event as independent. Are you sure that they are so highly dependent? $\endgroup$ – Francesco Pegoraro Sep 24 '18 at 14:35
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4$\begingroup$ Too old to migrate, but effectively duplicate: stats.stackexchange.com/questions/235087/… $\endgroup$ – Benji Albert Jul 19 '20 at 22:16
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Let $A$, $B$, $C$ be three (potentially dependent) events. By the probability chain rule: $$ P(A,B,C)=P(A|B,C)P(B,C)=P(A|B,C)P(B|C)P(C) $$ So we can do \begin{align} P(A|B,C) &= \frac{ P(A,B,C)}{P(B|C)P(C)} \\ &= \frac{ P(B,C|A) P(A) }{ P(B|C)P(C) } \\ &= \frac{ P(B|A,C) P(A) P(C) }{ P(B|C)P(C) } \\ &= \frac{ P(B|A,C) P(A) }{ P(B|C) } \end{align}
See this related post and this one as well.
