Mathematics

The key insight is to translate "mutually exclusive" into equations and then use them together. If $A$ and $B$ can't both happen, then $P(A \cap B) = 0$. But the second condition—that $A'$ and $B'$ are also mutually exclusive—tells you something about what must happen. Think about what it means for the complements to have no overlap, and how that constrains the original events.

The key insight is to translate "mutually exclusive" into equations and then use them together. If $A$ and $B$ can't both happen, then $P(A \cap B) = 0$. But the second condition—that $A'$ and $B'$ are also mutually exclusive—tells you something about what must happen. Think about what it means for the complements to have no overlap, and how that constrains the original events.