Complement
from class: Intro to Business Statistics Definition The complement of an event A in probability is the set of all outcomes in the sample space that are not in A. It is often denoted as $A^c$ or $\overline{A}$.
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Predict what's on your test 5 Must Know Facts For Your Next Test The probability of the complement of an event A, denoted $P(A^c)$, is calculated as $1 - P(A)$. If $P(A)$ is known, finding $P(A^c)$ can be a quick way to solve probability problems. The sum of the probabilities of an event and its complement is always equal to 1: $P(A) + P(A^c) = 1$. Complementary events are mutually exclusive; they cannot happen at the same time. Understanding complements can simplify complex probability questions by focusing on what does not happen. Review Questions How do you calculate the probability of the complement of an event A? What is the relationship between $P(A)$ and $P(A^c)$? Why are complementary events considered mutually exclusive? "Complement" also found in:
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