MGMT 2340 Section W01 Business Statistics I Instructor: E. Mark Leany contact via Blackboard online.uen.org alternately: [email protected] BASIC Probability you may already know Probability: 1/2 = 50% 1/6 = 17% 18/38 = 47% 18/38 = 47% 2/38 = 5% Outcome: Heads on a Coin Rolling a 6 on a die Red in Roulette Black in Roulette Everybody LOSES
A Survey of Probability Concepts Chapter 5 140 GOALS 1.Defineprobability. 2.Describe the classical, empirical, and subjective 3.Explain the terms experiment, event, outcome, permutations, and combinations. 4.Define the terms conditional probability andjointprobability. 5. Calculate probabilities using the rules of addition and rules of multiplication . 6. Apply a tree diagram to organize and compute probabilities. 7. Calculate a probability using Bayes’ theorem . 140
Refresher - Why Sample? z Sampling may destroy item z May not be possible to sample everything Same Reasons for Probability z Seldom have complete information Probability PROBABILITY A value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur. PROBABILITY A value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur. 142
Experiment, Outcome and Event z An experiment is a process that leads to the occurrence of one and only one of several possible observations. z An outcome is the particular result of an experiment. z An event is the collection of one or more outcomes of an experiment. 143 Mutually Exclusive Events and Collectively Exhaustive Events z Events are mutually exclusive if the occurrence of any one event means that none of the others can occur at the same time. z Events are collectively exhaustive if at least one of the events must occur when an experiment is conducted. z If exclusive and exhaustive: The SUM of the Probabilities = 100% 144
Ways of Assigning Probability There are three ways of assigning probability: 1. CLASSICAL PROBABILITY Based on the assumption that the outcomes of an experiment are equally likely. 2. EMPIRICAL PROBABILITY The probability of an event happening is the fraction of the time similar events happened in the past. 3. SUBJECTIVE CONCEPT OF PROBABILITY The likelihood (probability) of a particular event happening that is assigned by an individual based on whatever information is available. 147 Classical Probability Consider an experiment of rolling a six-sided die. What is the probability of the event “an even number of spots appear face up”? The possible outcomes are: There are three “favorable” outcomes (a two, a four, and a six) in the collection of six equally likely possible outcomes. 144
Empirical Probability The empirical approach to probability is based on what is called the law of large numbers. The key to establishing probabilities empirically is that more observations will provide a more accurate estimate of the probability.