# lect6 - Sample Space Event Probability Rules for...

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Sample Space, Event, Probability Rules for Probability Outline Sample Space, Event, Probability Classical Method Long-Run Relative Frequency Method Rules for Probability 1 / 17 ISOM 2500 Lect 6: Basic Concepts of Probability

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Sample Space, Event, Probability Rules for Probability Classical Method Long-Run Relative Frequency Method Sample Space An experiment is any process of observation with an uncertain outcome. Examples: 1. toss a coin: 2. roll a die: 3. play a football game 4. offer a loan The sample space of an experiment is the set of all possible outcomes that can happen, usually denoted by S . Examples: 1. toss a coin: {head, tail} 2. roll a die : {1,2,3,4,5,6} 3. play a football game: {win, loss, tie} 4. offer a loan: {default, late, on-time} 2 / 17 ISOM 2500 Lect 6: Basic Concepts of Probability
Sample Space, Event, Probability Rules for Probability Classical Method Long-Run Relative Frequency Method Event An event is a subset of the sample space, i.e., a set of possible outcomes Examples: 1. toss a coin: {head} 2. roll a die: {no more than 3} = { } 3. play a football game: {not a loss} = { } 4. offer a loan: {not a default} = { } 3 / 17 ISOM 2500 Lect 6: Basic Concepts of Probability

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Sample Space, Event, Probability Rules for Probability Classical Method Long-Run Relative Frequency Method Probability Probability is a measure of the chance that an outcome or an event will occur. If A is an outcome or an event, then P ( A ) denotes the probability that A will occur. A probability satisfies the following properties: 1. 0 P ( A ) 1 2. If A can never occur, then P ( A ) = 0 3. If A is certain to occur, then P ( A ) = 1 4 / 17 ISOM 2500 Lect 6: Basic Concepts of Probability
Sample Space, Event, Probability Rules for Probability Classical Method Long-Run Relative Frequency Method Assigning Probabilities to Outcomes/Events 1. Classical Method For equally likely outcomes 2. Long-run relative frequency Law of Large Numbers 3.

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