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Formal Probability

Formal Probability. Ch. 14. Basic Rules of Probability. The probability of any event is a number between 0 and 1. The set of all possible outcomes (the sample space S) must have a probability of 1. Basic Rules of Probability (cont.).

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Formal Probability

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  1. Formal Probability Ch. 14

  2. Basic Rules of Probability • The probability of any event is a number between 0 and 1. • The set of all possible outcomes (the sample space S) must have a probability of 1.

  3. Basic Rules of Probability (cont.) The set of all outcomes not in the event A is the complement of A or ~A • The probability of an event occurring is 1 minus the probability that it doesn’t occur.

  4. Basic Rules of Probability (cont.) Events that have no outcomes in common are disjoint (or mutually exclusive) • Addition Rule – For disjoint events, the probability that one or the other occurs is the sum of the probabilities of the two events

  5. Basic Rules of Probability (cont.) If the probability that an event will occur is not affected by the probability that another event has occurred, then the two events are independent. • Multiplication Rule – For two independent events, the probability that both events occur is the product of the probability of the two events.

  6. Independence Caveat • Many Statistics methods require an Independence Assumption, but assuming independence doesn’t make it true. • Always Think about whether that assumption is reasonable before using the Multiplication Rule.

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