Let $S$ be the sample space.
Let $A,B \subset S$ be two strict events with probability $p,q$ respectively.
The conditions are
Do there exist such $A,B$? If yes, how do they look like?
Using both the conditions and the identity $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ to an equation in $p,q$.
Solve for $p,q$ to get that $p=1$ or $q = 1$. But, $A,B$ are strict events. Hence, not possible.