Probability Rule C
The probability that an event does not occur is 1 minus the probability that the event does occur
Probability Rule C is also known as the Complement Rule. It states that the probability of an event E not happening (i.e. the complement of E, denoted as E’) is equal to one minus the probability of E happening. In mathematical notation, it can be expressed as:
P(E’) = 1 – P(E)
For example, if the probability of a student passing a test is 0.8, then the probability of them not passing is:
P(not passing) = P(failing) = 1 – P(passing) = 1 – 0.8 = 0.2
In general, the Complement Rule can be useful in situations where it’s easier to determine the probability of an event not happening rather than the probability of it happening. It’s also a key concept in probability theory and is used in many important probability theorems, such as the Law of Total Probability and Bayes’ Theorem.
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