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Lecture03Sept08 - Computing Probabilities Probability A...

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Computing Probabilities Sept. 08 Probability A probability measure is a function from the set of events to [0,1]. e.g. Roll 2 dice and record sum X Prob(X=10) Prob(X>10) Prob(X=10 or X<3) Probability – Formal Definition A probability measure is a function from the set of events to [0,1]: 1) P(A) ≥0 2) P(S)=1 3) If A 1 , A 2 ,... is a finite or countable set of events and A i A j = Ø for all pairs P(A 1 U A 2 U ... U A n ) = P(A 1 )+ P(A 2 )+...+ P(A n ) P(A 1 U A 2 U ...) = P(A 1 )+ P(A 2 )+... Basic Theorems Theorems: 1) P(A)=1-P(A’) 2) P(Ø)=0 3) If then P(A)≤P(B) 4) P(A) ≤ 1 5) P(A U B)=P(A)+P(B)-P(AB) B A 30% of the members of a fitness club are women. 40% of the members are doctors. 20% of the members are male doctors. If a member is selected at random (e.g. to complete a survey on customer satisfaction) what is the probability that the selected member is either a woman or a doctor? Basic Theorems Theorems: 1) P(A)=1-P(A’) 2) P(Ø)=0 3) If then P(A)≤P(B) 4) P(A) ≤ 1 5) P(A U B)=P(A)+P(B)-P(AB) Consider theorem 3.
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