Chapter 2 - Chapter 2 Probability Laws 1. A probability is...

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Chapter 2 – Probability Laws 1. A probability is always between 0 and 1. 0 ≤ P( A ) ≤ 1 2. The sum of the probabilities of all the events in the sample space S must equal 1. Σ P(A i ) = 1 Example: S = {A, B, C} so P(A) + P(B) + P(C) has to equal 1. 3. The complement of an event A includes all events that are not part of the event A. Denoted A (or sometimes A C ). Proof: A + A = S P(A) + P( A )= P(S) , where P(S)= 1 P( A ) = 1- P(A)
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Example of Complement Rule: Returning to the marble example: We have 4 Maroon and 7 Orange Marbles. We are selecting 3 marbles. What is the probability that at least one will be red?
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4. The Intersection of two events A and B is the set of all common outcomes of both A and B. The intersection is denoted by I . Ex. Roll a die Let A be the event of an odd number Let B be the event of a number at most 4 What is A I B? What is P(A I B )? A = { } B = { } A I B = { } P(A I B ) = # ways to get a # in both A and B Total # outcomes for rolling a die =
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5. The Union of two events A and B is the
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This note was uploaded on 08/25/2010 for the course STAT 4714 taught by Professor Mqlemons during the Fall '07 term at Virginia Tech.

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Chapter 2 - Chapter 2 Probability Laws 1. A probability is...

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