The opposite or complement of an event A is(that is, the event of A not occurring)is
$ P(A') = 1 - P(A)\, $
If two events, A and B are independent then the joint probability is
$ P(A \mbox{ and }B) = P(A \cap B) = P(A) P(B)\, $
If two events are mutually exclusive then the probability of either occurring is
$ P(A\mbox{ or }B) = P(A \cup B)= P(A) + P(B). $
If the events are not mutually exclusive then
$ \mathrm{P}\left(A \hbox{ or } B\right)=\mathrm{P}\left(A\right)+\mathrm{P}\left(B\right)-\mathrm{P}\left(A \mbox{ and } B\right). $
