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# LEC03 Probability and Addition Rule - Find the probability...

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Probability for experiments with discrete sample spaces 1

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Count Number of Elements in the Sample Space 2 Discrete S: elements in S can be counted with the integers 1, 2, 3, ... finite: flip a coin S={H, T} countably infinite: no. of calls in an hr S={0, 1, 2, ...} Continuous S: interval on the real line dimension of part S={(.90, 1.1)}
Examples: Are these discrete (finite or infinite) or Continuous? 3 S={a,b,c,d,f) S={2.1, 3.1, 6.125786} S={ (0.0, 0.0000001] } S={ (0, ) } S={1, 1/2, 1/3, 1/4, 1/5, 1/6, …} S={current inventory level of cars} S={current inventory level of road salt} S={state of machine – up, down, under repair}

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Defn of Probability for Experiments with Discrete Sample Spaces 4
Three Axioms: P(E) is the probability of event E 5

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6 Example: Parts can have two types of defects 10% of parts have defect A and 5% have defect B. 2% have both defects A and B. Find the probability a part has at least one

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Unformatted text preview: Find the probability a part has at least one defect. Given: event A = { part has defect A } P( A) = .10 Find Prob of at least one defect 7 Given: P( A) = .10 P( B) = .05 P(AB) = .02 Find: E ={at least one defect} = AB P(AB) Apply the addition rule: P (A B) = P(A) + P(B) - P(A B) Example: Two components in parallel 8 Given Component & System data The probability A works is 0.88 The probability B works is 0.71 The probability both work is 0.68 Find the probability the system works Given: P(A) = 0.88 P(B) = 0.71 Example: Analyze the results of inspected parts 9 Parts can have two types of defects, A and B. A sample of 150 parts are inspected an the results are shown below: Define notation; consider a randomly selected Defect B yes no Defec t A yes 5 10 no 15 120...
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