DS212_Chap4_Probability

DS212_Chap4_Probability - Chapter 4: Introduction to...

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1 Chapter 4: Introduction to Probability Sada Soorapanth Spring 2010
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2 What is Probability? Probability is a numerical measure of uncertainty or likelihood of an event. P(sunny tomorrow) = 0.7 Probability will always have a value between 0 and 1.
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3 Key Probability Terms Experiment : a process that produces outcomes. Sample space : the set of all possible outcomes of the experiment. Experiment Sample space (S) of experimental outcomes Toss a coin {Head, Tail} Record scores on a statistics test (out of 100) {0,1,2,…,100} Conduct a sales call {Purchase, no purchase} Roll a die {1,2,3,4,5,6} Play a football game {Win, lose, tie}
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4 Key probability terms Experimental outcome : an individual outcome of a sample space Test score of 67. Outcome of rolling a die =1 Event : a collection or set of one or more experimental outcomes in a sample space. Test scores of more than 80 = {81,82,. .100} Rolling an even number = {2,4,6}
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5 Basic requirements of probabilities Given a sample space of an experiment S = {e 1 ,e 2 ,e 3 ,…,e k }, 1. The probability of any outcome must be between 0 and 1, i.e. 0 ≤ P(e i ) ≤ 1 2. The sum of probabilities of all the outcomes in a sample space must be 1, i.e. ∑P(e i ) = 1
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6 Example #1: Assigning probability of events Three contractors (called them contractor 1,2, and 3) bid on a project to build a new bridge. What is the sample space? Suppose you believe that contractor 1 is twice as likely to win as contractor 3 and that contractor 2 is three times as likely to win as contractor 3. What are the probabilities of wining for each contractor? From Keller et al.
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7 Three approaches to assigning probabilities Classical method Probability of an event Number of outcomes consituting the event Total number of possible outcomes (or size of sample space) Probability of an event Sum of probabilities of outcomes constituting or = = the event.
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8 Three approaches to assigning probabilities (cont.) Relative frequency Historical data are available to estimate the proportion of the time the experimental outcome will occur. Subjective approach Based on expert’s judgment or experience
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9 Example #2: Assigning probability of events Consider the experiment of rolling a die. Find the probability of the following events An even number A number less than or equal to 4 A number greater than or equal to 5 From Keller et al.
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10 Example #3: Assigning probability of events The manager of a computer store has kept tract of the number of computers sold per day . Number of computers sold Relative frequency 0 0.08 1 0.17 2 0.26 3 0.21 4 0.18 5 0.1 From Keller et al.
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11 Example 3 (cont.) a) If we define the experiment as observing the number of computers sold tomorrow, determine the sample space. b) What is the probability of selling more than 3 computers?
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DS212_Chap4_Probability - Chapter 4: Introduction to...

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