Which of the following best describes the complement of event A?

The complement of an event is a key concept in probability theory that refers to all outcomes in which the event does not occur. When considering event A, the complement captures every possible outcome that isn't part of event A. This definition is foundational, as it helps in understanding events' probabilities in relation to each other.

For example, if event A represents rolling a die and getting a number greater than 4 (which includes 5 and 6), the complement of A would include all outcomes where you roll 1, 2, 3, or 4—essentially, every outcome that does not satisfy the condition of A.

This concept is crucial for calculating probabilities. The probability of the complement of an event can be found by subtracting the probability of the event from 1. In this context, knowing the complement allows statisticians to analyze scenarios more comprehensively and perform calculations effectively related to both the event and its complement.

The other options incorrectly define the complement, either by suggesting it includes outcomes where A occurs or by equating it to the probability or total outcomes, which do not accurately capture the relationship between an event and its complement. This distinction is vital for anyone studying probability and statistics.