In probability, what does the term "complement" refer to?

In probability, the term "complement" specifically refers to the probability of an event not occurring. If you have an event ( A ), the complement of ( A ), denoted as ( A' ) or ( \overline{A} ), consists of all outcomes in the sample space that are not included in ( A ).

Mathematically, if the probability of event ( A ) occurring is represented as ( P(A) ), then the probability of the event not occurring, which is the complement, is calculated by the formula:

[

P(A') = 1 - P(A)

]

This demonstrates that the sum of the probabilities of an event and its complement equals 1, highlighting the relationship between these two concepts. Thus, if the probability of a specific occurrence is known, the probability of its complement can be easily determined.

Having a clear understanding of complements is important for solving problems in probability, especially when dealing with events that have multiple possible outcomes or in scenarios where it's more practical to calculate the chances of something not happening rather than the event itself.