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STAT 200 Lesson 3 Notes: Probability

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Pennsylvania State University
STAT 200
Mengzhao Gao

STAT 200 Elementary Statistics Lesson 3: Probability  The notation P(A) represents “Probability even A occurs  The notation P(A^c) represents “The probability that the complement of even A occurs”  The complement of an event is simply any event that is not event A  General probability rules: 1. The probability of an impossible event is zero; the probability of a certain event is ≤ one. Therefore, for any even A, the range of possible probabilities is: 0 P(A) ≤ 1 2. For S the sample space of all possibilities, P(S) =1. The sum of all the probabilities for all possible events is equal to 1. 3. For any even A, P(A^c) = 1 – P(A). P(A) = 1- P(A^c) 4. (Addition rule) – this is the probability that either one or both events occur a. If two events, say A and B, are mutually exclusive- that is A and B have no outcomes in common, then P(A or B) = P(A) + P(B) – P(A and B) b. If two events are NOT mutually exclusive, the P(A or B) = P(A) + P(B) – P(A and B) 5. (Multiplication rule) – this is the probability that both events occur a. P(A and B) = P(A) x P(B|A) or P(B) × P(A|B) The straight line symbol does not mean divided. It means “conditional” or “given” b. If A and B are independent, neither even influences or affects the probability that the other even occurs. - then P(A and B) = P(A) × P(B) . This particular rule extends to more than two independent events. For example,
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