P(A) given that P(A|B) and P(B) are known Given that $P(A \mid B)$ is known, and $P(B)$ is known, how can $P(A)$ be calculated? I tried using the definition of conditional probability - $P(A \mid B) = P(A \cap B)/ P(B)$ - to solve for $P(A \cap B)$ but I don't know where to go from there. Any hints? 

In general, you can't calculate $P(A)$ from just $P(A \mid B)$ and $P(B)$ — you also need to know $P(A \mid \lnot B)$.
If you do know that, the calculation is easy enough:
$$\begin{aligned}P(A) 
&= P(A \land B) + P(A \land \lnot B) \\
&= P(A \mid B)P(B) + P(A \mid \lnot B)P(\lnot B) \\
&= P(A \mid B)P(B) + P(A \mid \lnot B)(1 - P(B))
\end{aligned}$$
