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• A probability model for a random phenomenon consists of a sample space S and an assignment of probabilities P.
• The sample space S is the set of all possible outcomes of the random phenomenon. Sets of outcomes are called events. P assigns a number P(A) to an event A as its probability.
• The complement Ac of an event A consists of exactly the outcomes that are not in A. Events A and B are disjoint if they have no outcomes in common. Events A and B are independent if knowing that one event occurs does not change the probability we would assign to the other event.
• Any assignment of probability must obey the rules that state the basic properties of probability:
Rule 1. 0 ≤ P(A) ≤ 1 for any event A.
Rule 2. P(S) = 1.
Rule 3. Addition rule: If events A and B are disjoint, then P(A or B) = P(A) + P(B).
Rule 4. Complement rule: For any event A, .
Rule 5. Multiplication rule: If events A and B are independent, then P(A and B) = P(A)P(B).