Sum rule (m+nm+n)
If outcome AA can be chosen in mm ways, BB in nn ways, and choosing both AA and BB in one “case” is impossible, then “AA or BB” happens in m+nm+n ways. Phrases like “or…”, “either…”, “in one of mutually exclusive scenarios” signal a sum (after checking AB=A\cap B=\varnothing in the intuitive sense of the problem).
If cases overlap, naive m+nm+n overcounts — you need inclusion–exclusion or another model
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