# Determining disjointness via given probabilities of two events

Given probabilities, $\mathbb{P}(A)$ and $\mathbb{P}(B)$, of events $A$ and $B$, can we determine mutual exclusiveness of the two events?

-

If $\Bbb P(A)+\Bbb P(B)>1$, then clearly $A\cap B\ne\varnothing$: they can’t be mutually exclusive. Otherwise, though, we can’t say anything without further information.