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Unformatted text preview: Introduction to Probability GE 331/IE300 Glser Kksal UIUC IESE 2011 2 G.Kksal, UIUC IESE, 2011 2 Contents Experiments, Counting Rules, and Assigning Probabilities Events and Their Probability Some Basic Relationships of Probability Conditional Probability Bayes Theorem 3 G.Kksal, UIUC IESE, 2011 3 Uncertainties We often face with decision making under uncertainties: What are the chances that sales will decrease if we increase prices? What is the likelihood a new assembly method will increase productivity? What are the odds that a new shipment of zippers to a textiles plant contains more defective items than we can accept? 4 G.Kksal, UIUC IESE, 2011 4 Probability Probability is a numerical measure (between 0 and 1) of the likelihood that an event will occur. Provides ways to quantify likelihood of events . It helps us make effective decisions under uncertainty. 5 G.Kksal, UIUC IESE, 2011 5 Statistical Experiments In statistical experiments, probability determines outcomes . Even though the experiment is repeated in exactly the same way, an entirely different outcome may occur. For this reason, statistical experiments may be called random experiments . 6 G.Kksal, UIUC IESE, 2011 6 An Experiment and Its Sample Space Experiment Toss a coin Inspect a part Conduct a sales call Roll a die Play a football game Experimental Outcomes Head, tail Defective, nondefective Purchase, no purchase 1, 2, 3, 4, 5, 6 Win, lose, tie Sample space 7 G.Kksal, UIUC IESE, 2011 7 Consider a bottling operation that has two possible outcomes: defective items, nondefective items Defective items might be of 4 types: U: Underfilled C: Cap missing B: Bar code missing L: Label missing Example: Bottles An Experiment and Its Sample Space http://www.youtube.com/watch?v=nip1akEAU4Y&feature=related 8 G.Kksal, UIUC IESE, 2011 8 A Counting Rule for MultipleStep Experiments If an experiment consists of a sequence of k steps in which there are n 1 possible results for the first step, n 2 possible results for the second step, and so on, then the total number of experimental outcomes is given by ( n 1 )( n 2 ) . . . ( n k ) 9 G.Kksal, UIUC IESE, 2011 9 If two bottles are inspected, what is the total number of outcomes? Bottle 1: n 1 = 5 Bottle 2: n 2 = 5 Total number of experimental outcomes: n 1 n 2 = (5)(5) = 25 A Counting Rule for MultipleStep Experiments Example: Bottles 10 G.Kksal, UIUC IESE, 2011 10 Tree Diagram First bottle Experimental outcomes U OK B C L U OK B C L ... ... ... ... (OK, OK) (OK, U) (OK, C) (OK, B) (OK, L) Second bottle Example: Bottles ... 11 G.Kksal, UIUC IESE, 2011 11 Number of Permutations of N Objects Taken n at a Time where: N ! = N ( N 1)( N 2) . . . (2)(1) n ! = n ( n 1)( n 2) . . . (2)(1) 0! = 1 Counting Rule for Permutations This rule enables us to count the number of experimental outcomes when n objects are to be selected from a set of N objects, where the order of selection is important....
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 Spring '09
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