AxiomsOfProbability - If the coin and dice are both fair,...

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Learning Objectives State the three axioms of probability.
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Example After an exam, a doctor concludes that a patient has either plague, leprosy, or SARS. She decides that the probability is 0.7 that the patient has plague, 0.2 that the patient has leprosy, and 0.1 that the patient has SARS. What is the probability that the patient has either plague or leprosy?
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Axioms of Probability Non-negativity Additivity Normalization
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Non-negativity For every event A, P ( A ) ³ 0
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Additivity The probability of the union of disjoint events is the sum of their individual probabilities P ( A 1 È A 2 È ...) = P ( A 1 ) + P ( A 2 ) +. ..
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Normalization The probability of the entire sample space ( ) is equal to one P (W) =1
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Example Experiment: flip a coin and roll a six-sided dice Sample space (outcomes): ={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}
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Unformatted text preview: If the coin and dice are both fair, then each of the 12 outcomes is equally likely. Additivity & normalization -> P({})=1/12 Example Calculate probabilities of events by counting the number of outcomes and dividing by the total number of outcomes P(A) = 6/12 P(B) = 6/12 P(C) = 2/12 A = H 1, H 2, H 3, H 4, H 5, H 6, { } B = H 1, H 3, H 5, T 1, T 3, T 5 { } C = H 3, T 3 { } Does this conflict with the additivity axiom? More Probability Properties P() = 0 P(A c ) = 1 - P(A) If A B then P(A) P(B) P(B) = P(A B) + P(A c B) P(A B) = P(A) + P(A c B) P(A B) = P(A) + P(B) - P(A B) P(A B C) = P(A) + P(A c B) + P(A c B c C) Exercises Exercise #1 Exercise #2 Exercise #3...
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This note was uploaded on 02/01/2011 for the course BME 335 taught by Professor Dunn during the Spring '10 term at University of Texas at Austin.

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AxiomsOfProbability - If the coin and dice are both fair,...

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