# Lecture5 - lecture 5 Probability I 1/29 Experiment Sample...

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Unformatted text preview: lecture 5, Probability I 1/29 Experiment, Sample Space and Event The Concept of Probability Classical Method Long-Run Relative Frequency Method Subjective Probability Some Event Operations and Elementary Probability Rules lecture 5, Probability I Outline 1 Experiment, Sample Space and Event 2 The Concept of Probability Classical Method Long-Run Relative Frequency Method Subjective Probability 3 Some Event Operations and Elementary Probability Rules lecture 5, Probability I 2/29 Experiment, Sample Space and Event The Concept of Probability Classical Method Long-Run Relative Frequency Method Subjective Probability Some Event Operations and Elementary Probability Rules lecture 5, Probability I Experiment, Sample Space and Event Experiment An experiment is any process of observation with an uncertain outcome • Examples: • toss a coin • roll a die • draw a card • play a football game • ... lecture 5, Probability I 3/29 Experiment, Sample Space and Event The Concept of Probability Classical Method Long-Run Relative Frequency Method Subjective Probability Some Event Operations and Elementary Probability Rules lecture 5, Probability I Experiment, Sample Space and Event Sample Space The sample space of an experiment is the set of all possible outcomes , usually denoted by S • Examples: 1 toss a coin: {a head, a tail} 2 roll a die: {1,2,3,4,5,6} 3 draw a card: {ace of clubs, ace of diamonds, ace of hearts, ace of spades, 2 of clubs,..., king of spades} 4 play a football game: {win, loss, tie} lecture 5, Probability I 4/29 Experiment, Sample Space and Event The Concept of Probability Classical Method Long-Run Relative Frequency Method Subjective Probability Some Event Operations and Elementary Probability Rules lecture 5, Probability I Experiment, Sample Space and Event Example: Genders of Two Children A newly married couple plans to have 2 children • What’s the sample space? • The sample space S = { } lecture 5, Probability I 5/29 Experiment, Sample Space and Event The Concept of Probability Classical Method Long-Run Relative Frequency Method Subjective Probability Some Event Operations and Elementary Probability Rules lecture 5, Probability I Experiment, Sample Space and Event Event An event is a subset of the sample space, i.e., a set of possible outcomes • Examples: 1 toss a coin: {a head} 2 roll a die: {no more than 3} = { } 3 draw a card: {ace} = {ace of spades, ace of diamonds, ace of hearts, ace of clubs} 4 Play a football game: {not a loss} = { } lecture 5, Probability I 6/29 Experiment, Sample Space and Event The Concept of Probability Classical Method Long-Run Relative Frequency Method Subjective Probability Some Event Operations and Elementary Probability Rules lecture 5, Probability I Experiment, Sample Space and Event Genders of Two Children ( ctd) Sample space S = { BB , BG , GB , GG } The event {one boy and one girl} = {at least one girl} = . lecture 5, Probability I 7/29 Experiment, Sample Space and Event The Concept of Probability...
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Lecture5 - lecture 5 Probability I 1/29 Experiment Sample...

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