One way to check whether two events are independent is with the formula $P(A\mathrm{\&}B)=P(A)\ast P(B)$. If this holds, the two events are independent (to my knowledge).

Now if $A$ and $B$ are mutually exclusive events, and $P(A)>0$ and $P(B)>0$, then $P(A\mathrm{\&}B)=0\ne P(A)\ast P(B)$, and thus the events are considered dependent. Why does this make intuitive sense?

Now if $A$ and $B$ are mutually exclusive events, and $P(A)>0$ and $P(B)>0$, then $P(A\mathrm{\&}B)=0\ne P(A)\ast P(B)$, and thus the events are considered dependent. Why does this make intuitive sense?