The probability of an event $B$ is $P_1$. The probability that events $A$ and $B$ occur together is $P_2$ while the probability that $A$ and $\bar{B}$ occur together is $P_3$. The probability of the event $A$ in terms of $P_1, P_2$ and $P_3$ is _____________
$P(A \cap \sim B)$=Something that is in A but not in B.
And Since, P(B)=$P_1$ and $P(A\cap B)=P_2$, the region which is only in B has probability $P_1-P_2$
so, $P(A)=P_3+P_2$
Solving using venn diagram looks easier.
3p_{2}+p_{1}-p_{2}