Bayes Theorem for Conditional event that is an intersection of independent events.

Question

I have a question regarding Bayes theorem, and independent intersected events as the conditional. How can this probability be decomposed using Bayes?

$P(H \mid E \cap R)$ where $E$ and $H$ are independent events.

Does that equal $P(H\mid E)\cdot P(H\mid R)$?

No. Let $R$ also be independent of $H$. Then you're asking if $P(H)=P(H)\cdot P(H)$ — T.J. Gaffney, Oct 29 '14 at 03:22

score -1 · Accepted Answer · edited Mar 31 '16 at 09:49

-1

$P(H|E,R) = P(H,E,R)/P(E,R)$

$ P(H,E,R) = P(H|E,R)/P(E,R)$

edited Mar 31 '16 at 09:49

Watson

answered Nov 16 '15 at 00:25

Jeff Grover

1 Answers1