and are two events in a sample space of a
random experiment, where . Given that , determine .
The events and are complementary, so the sum of their
probabilities is equal to 1. First, use this fact to find
probability of .
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 . Now use this fact to solve for .
The notation refers to the probability of either event or
event occurring, or both. Next, solve for .
If and are two non-mutually exclusive events, then . Finally,
use this fact to find the probability of .
Thus, the probability of is 0.286.