What does the complement of an event refer to?

The complement of an event refers specifically to the situation where the event does not occur. In probability theory, if you have an event A, the complement of A encompasses all outcomes in the sample space that are not part of A. This is crucial in understanding probabilities because it allows one to easily calculate the likelihood of an event not occurring by subtracting the probability of the event from 1.

For example, if the probability of event A occurring is 0.7, then the probability of the complement of A (not A occurring) is 1 - 0.7 = 0.3. This principle is foundational in probability, as it helps to facilitate calculations and provides insights into the relationships between different possible outcomes. It also highlights the comprehensive nature of probabilities, as every possible outcome must either be part of an event or its complement.