Given that , , and are three mutually exclusive events in a sample space of a random experiment, where , , and , determine .
First, solve for in terms of as follows:
Since events , , and are mutually exclusive, and they make up the sample space, the sum of their probabilities must be equal to 1.
Now use this fact, along with substitution, to find the probability of .
Next, use the fact that to find the probability of .
The notation refers to the probability of either event or event occurring.
If and are two mutually exclusive events, then . Finally, use this fact to determine the probability of as follows:
Thus, is equal to .