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The Complete Idiot's Guide to Statistics, 2nd Edition by Robert Donnelly

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Addition Rule of Probabilities

We use the addition rule of probabilities to calculate the probability of the union of events—that is, the probability that either Event A or Event B will occur. For two events that are mutually exclusive, the addition rule states the following:
P[A or B] = P[A] + P[B]
As an example, for the single-die experiment with mutually exclusive events:
◆ Event A: Roll a 1.
◆ Event B: Roll a 2.
def•i•ni•tion
For mutually exclusive events, the addition rule states that P[A or B] = P[A] + P[B]. If the events are not mutually exclusive, the addition rule becomes P[A or B] = P[A] + P[B] - P[A and B].
The simple probabilities are as follows:
and
The probability that either a 1 or a 2 will be rolled ...

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