# Lect5 - Experiment, Sample Space and Event The Concept of...

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Experiment, Sample Space and Event Outline 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 Complement Union and Intersection Addition Rule 1 / 29 Xinghua Zheng Probability I

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Experiment, Sample Space and Event Experiment ± An experiment is any process of observation with an uncertain outcome I Examples: 1. toss a coin 2. roll a die 3. draw a card 4. play a football game 5. ... 2 / 29 Xinghua Zheng 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 I 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} 3 / 29 Xinghua Zheng Probability I

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Experiment, Sample Space and Event Example: Genders of Two Children ± A newly married couple plans to have 2 children I The sample space S = { } 4 / 29 Xinghua Zheng Probability I
Experiment, Sample Space and Event Event ± An event is a subset of the sample space, i.e., a set of possible outcomes I 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} = { } 5 / 29 Xinghua Zheng Probability I

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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} = . 6 / 29 Xinghua Zheng Probability I
Experiment, Sample Space and Event Classical Method Long-Run Relative Frequency Method Subje c Probability ± Probability is a measure of the chance that an outcome or an event will occur when an experiment is carried out I If E is an outcome or an event, then P ( E ) denotes the probability that E will occur. ± A probability satisﬁes the following properties: 1. 0 P ( E ) 1 2. If E can never occur, then P ( E ) = 0 3. If E is certain to occur, then P ( E ) = 1 4. The probabilities of all the possible outcomes sum to 1 7 / 29 Xinghua Zheng Probability I

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Experiment, Sample Space and Event Classical Method Long-Run Relative Frequency Method Subje c Assigning Probabilities to Outcomes/Events 1. Classical Method ± For equally likely outcomes 2. Long-run relative frequency 3. Subjective probability ± Assessment based on experience, expertise or intuition 8 / 29 Xinghua Zheng Probability I
Experiment, Sample Space and Event Classical Method Long-Run Relative Frequency Method Subje c Classical Method ± If all the possible outcomes are equally likely to occur, then the probability of any outcome ω is P [ ω ] = 1 # all possible outcomes = 1 | S

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## This note was uploaded on 12/28/2010 for the course ISOM ISOM111 taught by Professor Anthonychan during the Fall '09 term at HKUST.

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Lect5 - Experiment, Sample Space and Event The Concept of...

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