College Math Placement Practice Test

In probability, what does the complement of an event represent?

1. The event occurring

2. The event not occurring

3. The outcome of the event

4. The total probability

The correct answer is: The event not occurring

The complement of an event in probability represents all the outcomes in the sample space that do not include the event occurring. When we talk about an event, we often denote it as \( A \). The complement of \( A \), typically written as \( A' \) or \( \bar{A} \), encompasses every possible outcome except for those where event \( A \) occurs. For instance, if the event \( A \) describes rolling a 3 on a six-sided die, then the complement \( A' \) would include all other results—rolling a 1, 2, 4, 5, or 6. Understanding the complement is crucial in probability because it allows us to calculate the likelihood of an event not occurring, which can sometimes be easier than calculating the probability of the event occurring directly. In probability, the sum of the probabilities of an event and its complement always equals 1. This concept is fundamental to reasoning about probability and is widely applicable in various scenarios. Thus, the correct interpretation of the complement of an event is that it represents the event not occurring.