Talk:Complementary event

Mathematical error

Someone seems to be under the impression that if Pr(A) + Pr(B) = 1 then A and B are complementary. That is not true. For example, suppose one randomly chooses a number from the set { 1, 2, 3, 4}, the four numbers being equally probable. The probability that one gets 1 is 1/4, and the probability that one gets either 1, 2, or 3 is 3/4 so the sum of the two probabilities is 1. But obviously these events are not complementary; the complement of {1} is {2, 3, 4}, not {1, 2, 3}. Michael Hardy 01:19, 6 October 2005 (UTC)