What Complement rule is
The Complement Rule is a statistical rule stating that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. For example, the probability of rolling a six on a six-sided die is 1/6. Therefore, the probability of not rolling a six is 1 - 1/6 = 5/6.
The complement rule can be used to calculate probabilities for events that are mutually exclusive. For example, if you wanted to calculate the probability of rolling a number other than a six on a six-sided die, you can use the complement rule. The probability of not rolling a six is 5/6 and since the probability of rolling any other number is mutually exclusive, the probability of rolling a number other than a six is 5/6.
Steps for Complement Rule:
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Identify the event that you are trying to calculate the probability of.
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Calculate the probability of the event occurring.
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Calculate the probability of the event not occurring by using the complement rule: 1 minus the probability of the event occurring.
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The result is the probability of the event not occurring.
Examples
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The complement rule is often used to find the probability of an event not occurring. For example, if the probability of an event occurring is 0.2, then the probability of it not occurring is 0.8 (1 - 0.2 = 0.8).
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The complement rule can also be used to help calculate probabilities of mutually exclusive events. For example, if the probability of event A occurring is 0.4 and the probability of event B occurring is 0.3, then the probability of either event not occurring is 0.7 (1 - 0.4 - 0.3 = 0.7).