Lecture 2a Introduction to Probability

Lecture 2a Introduction to Probability - Lecture 2...

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Lecture 2 Introduction to Probability Source: /1 / D.R.Anderson, D.J.Sweeney, T.A.Williams. Quantitative Methods for Business, South-Western College Publishing, 11-th edition. Chapter 2. Contents: 2.1 Experiments and the sample space 2.2 Assigning probabilities to experimental outcomes 2.3 Events and their probabilities 2.4 Some basic relationships of probability Business decisions are often based on an analysis of uncertainties such as the following: 1. What are the "chances" that sales will decrease if we increase prices? 2. What is the "likelihood" that а new assembly method will increase productivity? 3. How “likely’’ is it that the project will be completed on time? 4. What are the "odds" in favor of а new investment being profitable? Probability is а numerical measure of the likelihood that an event will occur. Thus, probabilities could be used as measures of the degree of uncertainty associated with the four events previously listed. If probabi1ities were available, we could determine the likelihood of each event occurring. Probability values are always assigned on а scale from 0 to 1. А probability near 0 indicates that an event is unlikely to occur; а probability near 1 indicates that an event is almost certain to occur. Other probabilities between 0 and 1 represent varying degrees of likelihood that an event will occur. Probability is important in decision making because it provides а way to measure, express, and ana1yze the uncertainties associated with future events. 2.1 Experiments and the Sample space Experiment is a process that generates well-defined outcomes . (On any single repetition of an experiment one and only one of possible experimental outcomes will occur) The set of all possible experimental outcomes is called the Sample Space . Particular experimental outcome is called the Sample Point ( or Simple Event) Sample Point ( or Simple Event) can not be decomposed into a simpler outcome. Examples 2.1 : Experiment Sample space i E are experimental outcomes(sample points) 1. Tossing 1 coin { } 2 1 , E E where 1 E Head (H), 2 E Tail (T) 1
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2. Tossing 3 coins at once where { } THH HTT HTH THT HHT TTH TTT HHH , , , , , , , 8 4 7 3 6 2 5 1 8 7 6 5 4 3 2 1 E E E E E E E E E E E E E E E E 3. Rolling a fair die where { } 6 3 5 2 4 1 , , , , , 6 3 5 2 4 1 6 5 4 3 2 1 E E E E E E E E E E E E 4. Conducting a sales call { } 2 1 , E E where 1 E - the customer purchases the product, 2 E - the customer does not purchase the product. 2.2 Assigning probabilities to experimental outcomes The probability of an experimental outcome is a numerical measure of the likelihood that the experimental outcome will occur. How probabilities for the experimental outcomes can be determined?
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Lecture 2a Introduction to Probability - Lecture 2...

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