Given that the English alphabet letters is a sample space of 26 letters, , and , find
The notation refers to the probability of the occurrence of and the non-occurrence of .
There are no common elements in and , so they are mutually exclusive events, and they can never occur together.
For this reason, is equal to . The probability of event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space, . First, find the probability of event as follows:
The events and are complementary, so the sum of their probabilities is equal to 1. Now use this fact to find the probability of .
Since is equal to , it follows that is equal to . Thus, is equal to .