The complement of an event is the set of all outcomes in the sample space that are not part of the event. It is denoted as $E'$ or $E^c$ for an event $E$.
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The probability of the complement of an event is given by $P(E') = 1 - P(E)$.
If an event $E$ is certain, then its complement has a probability of zero.
If two events are mutually exclusive and exhaustive, their probabilities sum to one.
The complement rule can simplify calculations, especially when it is easier to calculate the probability of the complement rather than the event itself.
The union of an event and its complement covers the entire sample space.
Review Questions
What is the formula to find the probability of the complement of an event?
How does knowing the complement help in calculating probabilities?
Explain what it means for two events to be mutually exclusive and exhaustive.
Related terms
Sample Space: The set of all possible outcomes in a probability experiment.
Mutually Exclusive Events: Two events that cannot occur at the same time.
Probability: A measure quantifying the likelihood that events will occur; ranges from 0 to 1.