# Lecture 4 - Lecture4 Probability LearningObjectives...

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Lecture 4 Probability Probability

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Learning Objectives Comprehend  the different ways of assigning  probability Understand and apply  marginal, union, joint, and  conditional probabilities Select  the appropriate law of probability to use in  solving problems Solve  problems using the laws of probability  including the laws of addition, multiplication and  conditional probability Revise  probabilities using Bayes’ rule
Introduction Generally, business decision making is  based on an uncertain environment. We  can use probability concepts to determine  the likelihood of particular outcomes Other specific applications are in the  gambling and insurance industries

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Methods of Assigning  Probabilities Classical method of assigning probability  (rules and laws) Relative frequency of occurrence  (cumulated historical data) Subjective probability (personal intuition  or reasoning)
Classical Probability Number of outcomes leading to  the event  divided by the total  number of outcomes possible Each outcome is equally likely Determined  a priori  - before  performing the experiment Applicable to games of chance occurs event he in which t outcomes of number the outcomes of number total : ) ( = = = e e n N where N n E P

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Classical Probability The highest value of any probability is 1 – this  event is certain to occur The lowest value of any probability is 0 – this  event is certain not to occur 0 ( ) 1 P E ≤ ≤
Relative Frequency  Probability Based on historical  data Computed after  performing the  experiment Number of times an  event occurred divided  by the number of trials P(E) =  where:   N  = total number of  opportunities for an event  to occur x  = number of times an event  occurred x N

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Subjective Probability Comes from a person’s intuition or reasoning Subjective - different individuals may (correctly)  assign different numeric probabilities to the same  event Degree of belief Useful for unique (single-trial) experiments New product introduction Initial public offering of common stock Site selection decisions Sporting events
Structure of Probability Experiment Event Elementary Events Sample Space Unions and Intersections Mutually Exclusive Events Independent Events Collectively Exhaustive Events Complementary Events

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Experiment Experiment: a process that produces outcomes More than one possible outcome Only one outcome per trial Trial: one repetition of the process Event: an outcome of an experiment (usually
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Lecture 4 - Lecture4 Probability LearningObjectives...

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