I read that the probability that at least one of events A and B will occur in a trial is P(A + B) = P(A) + P(B) - P(AB), where A and B are **not** mutually exclusive events. That makes sense, because one would count the probabilities of A and B together, and then ignore event AB, because that counts instances of A and B twice, in the same way that the probability that at least one die of two will turn up six is 11/36, not 1/3.

That made sense intuitively, but I couldn't quite follow the proof because it mentioned things I never saw before. I noticed however, that the following relation also appears to be true (A_{C} and B_{C} are complementary events because latex2html is a dick.)

P(A_{C}B_{C}) + P(AB) + P(A_{C}B) + P(AB_{C}) = 1

P(AB) + P(A_{C}B) + P(AB_{C}) = 1 - P(A_{C}B_{C})

and so

P(A + B) = 1 - P(A_{C}B_{C})

I did it on some practice examples and it made sense, but what do I know...