Are 2 dependent probabilities always disjunct? If $2$ probabilities are disjunct then they are not independent. Are any $2$ dependent probabilities also disjunct? Modus ponens for instance are $2$ dependent and mutually exclusive events ($A$ and $B$) where $B$ occurs if and only if $A$ occurred prior to B. Did I misunderstand? Can you please let us know a good example or counter-example? I think that disjunct in this case means "cannot occur at the same time". $P(\text{head})$ and $P(\text{tail})$ for an even coin is $50:50$ and the outcomes of $2$ throws are typically independent events ($0.5\cdot 0.5$ for $2$ throws per outcome). Can we elaborate how the statement is not a tautology and some probabilities can be dependent **and** disjunct?

I am assuming that disjunct probabilities mean that the events are mutually exclusive (disjoint as sets). Dependent probabilities need not be 'disjunct'. For example, roll a die twice.

Let $A$ be the event that the first roll is $4$ and let $B$ be that the sum is $5$.

$P(A)=\frac16$. $P(B)=\frac4{36}$. And $P(A\cap B)=\frac{1}{36}\
e P(A)P(B)$

So $A$ and $B$ are dependent, but not disjoint (mutually exclusive).