Premise: My understanding is that if two events are mutually exclusive, it need not be that they are complementary. However I came across a question that said the following - If $P(A') = \alpha$ and $P(B') =\beta$ then $P( A\cap B)$ must be ?
The answers is greater than or equal to $1 - \alpha- \beta$. I get the idea, but what if $A$ and $B$ are mutually exclusive - Wouldn't the answer given be wrong then? Because my premise is that disjoint does not mean $\alpha + \beta = 1$, so $1 - \alpha- \beta$ would have a positive value clearly not equal to zero!.