and are two events in a sample space of a random experiment, where , , and . Find .
The notation refers to the probability of the occurrence
of and the non-occurrence of Also, the notation refers to the probability of events and occurring
together. For this reason, is equal to the sum of and First, use this fact to solve for
Since and are complementary, the sum of their probabilities is
equal to 1. Now use this fact to find the probability of
De Morgan's second law states that where the notation means the
non-occurrence of or the non-occurrence of or both. Since it follows that