Two events A and $B$ have $P(A)=0.5$ and $P(B)=0.3$. Let $x$ be the value of $P$(A or B) when A and $B$ are independent, and let $y$ be its value when A and $B$ are mutually exclusive instead. What is $y-x$?

Mutually exclusive means the two cannot both happen, so $P$(A and B) = 0 and $y=0.5+0.3-0=0.80$. Independent means $P$(A and B) = $P(A)\times P(B)=0.5\times 0.3=0.15$, so $x=0.5+0.3-0.15=0.65$. Hence $y-x=0.80-0.65=0.15$, which is precisely the overlap that independence creates and mutual exclusivity forbids. The two ideas are not variations of the same thing: two events with non-zero probabilities that are mutually exclusive can never be independent, because knowing one has happened makes the other impossible. Traps 0.80 and 0.65 each quote one of the two values instead of the difference asked for. Trap 0.35 = 0.5 − 0.15 subtracts the overlap from $P$(A) alone.