P(A and B) = 0, which makes P(A or B) = P(A) + P(B) with no correction term.
The trap. Mutually exclusive events are the opposite of independent, not a form of it. If A and B cannot co-occur and both have positive probability, then learning A happened tells you B did not - maximal dependence.
Candidates asked "are these independent or mutually exclusive?" who treat the terms as interchangeable are demonstrating a real gap, which is why the question gets asked.