I have P(B|A) and P(A), there isn't a quick way to get P(B) off this is there?
A and B are not independent.
Thanks,
Brendan
Hello, Brendan!
I have $\displaystyle P(B|A)$ and $\displaystyle P(A).$
There isn't a quick way to get $\displaystyle P(B)$ off this, is there? . no
$\displaystyle \,A$ and $\displaystyle \,B$ are not independent.
From Bayes' Theorem, we have: .$\displaystyle P(B|A) \;=\;\dfrac{P(A \cap B)}{P(A)} $
. . Hence: .$\displaystyle P(A \cap B) \;=\;P(B|A)\cdot P(A)$
But without more information, such as $\displaystyle P(A \cup B)$,
. . we cannot isolate $\displaystyle P(B).$