INFO 1020 Business Statistics and Analysis Welcome Back Chapter 4 Probability Theory Agenda Introduction Syllabus Blackboard Chapter 4 Probability Theory INFO Sequence Journey Welcome to INFO 1020 This is the second of a 3 courses program in DCB INFO 1010 Data Management and Analysis INFO 1020 Business Statistics and Analysis INFO 2020 Business Modeling and Analysis Your Professor Dr Young Jin Lee Go by Young Jin or YJ either way Born and raised in S Korea BS in Business Ohio State U MISM Carnegie Mellon U Ph D in Business University of Washington Married 2 kids Past employment Industry Samsung Academia U of Washington and U of Wisconsin Research interests Economics of social media and mobile computing Digital right managements Innovation of technology adoption Goals of INFO 1020 Fundamentals of probability Statistical inference Business decision making Statistics in Business What is Statistics interpreting data The art of science of collecting analyzing presenting and How do we use this in our daily life Example Why do we in business refer to numerical facts A better understanding of the business and economic environment more informed and better decisions to decision makers and managers IT technologies Database Data mining Business Intelligence Big Data Analytics etc Why Business Analytics and Big Data Volume Velocity Variety Tremendous business opportunity Data experts are In high demand Well compensated secure Similar to INFO 1010 Still heavy use of Excel Project based Dealing with data Still tied to business Different from INFO 1010 Relatively smaller datasets Traditional statistics for business coverage Data are processed to help business decision processes Blackboard Can you log in Can you find our course in Blackboard You should be familiar with this by now Let s take a quick tour of the site Syllabus Let s walk through it Book Still same book Good for 3 quarters Hands on reference Starting with Chapter 4 Business Information and Analytics Course Structure Readings Outside of Class Highly recommended Homework tied to lecture Necessary to participate in class Lot of hands on work Course project Business Information and Analytics Excel We are going to build on our knowledge of Excel Certification Anyone still not passed the Excel Business Information and Analytics Homework Online homework will be assigned most classes and will due before the following class period There would be 15 assignments and they will be posted in each module in our Blackboard site 9 highest scores will be calculated for Homework 10 Late work will be accepted with a penalty up to one week late Business Information and Analytics Project One project that takes us from beginning to end of course Let s see and example or 2 Let s walk through it Business Information and Analytics How Do We Get to Decisions DATA Make Decision Basic Data Analysis 1010 Statistical Analysis 1020 Analytic Modeling 2020 Business Information and Analytics Introduction to Probability Topics for today Experiments Counting Rules and Assigning Probabilities Prerequisite Statistical Analysis Probability Powerball Coin Flipping Business Information and Analytics Uncertainty Managers often base their decisions on an analysis of uncertainties such as the following What are the chances that sales will decrease if we increase prices What is the likelihood a new assembly method will increase productivity What are the odds that a new investment will be profitable Probability Probability is a numerical measure of the likelihood that an event will occur Probability values are always assigned on a scale from 0 to 1 A probability near zero indicates an event is quite unlikely to occur A probability near one indicates an event is almost certain to occur Q Can probability be ever less than 0 and greater than 1 1 Yes It Depends 2 No Never Statistical Experiments In statistical experiments probability determines outcomes of experiment Even though the experiment is repeated in exactly the same way an entirely different outcome may occur For this reason statistical experiments are sometimes called random experiments Experiment and Sample Space An experiment is any process that generates well defined outcomes The sample space for an experiment is the set of all experimental outcomes An experimental outcome is also called a sample point Q When you conduct an experiment of rolling a dice the sample space includes 1 1 2 6 2 1 2 3 4 5 6 3 2 3 4 4 1 2 3 Q Tossing two coins together is an experiment and the sample space includes 1 HH TT HT TH 2 H T 3 H T H T Other Examples Experiment Toss a coin Experiment Outcomes Head tail Inspection a part Defective non defective Conduct a sales call Purchase no purchase Roll a die 1 2 3 4 5 6 Play a football game Win lose tie Counting Rules Identifying and counting the experimental outcomes in order to assign probabilities 1 Multiple Step Experiments 2 Combinations 3 Permutations Multiple Step Experiments If an experiment consists of a sequence of k steps in which there are n1 possible results for the first step n2 possible results for the second step and so on then the total number of experimental outcomes is given by n1 n2 nk A helpful graphical representation of a multiple step experiment is a tree diagram Q If Tim has one ball from 2 balls to choose from and Paul has one ball from 4 balls to choose from in how many ways can they collectively make the decision of choosing two balls one each 1 2 2 4 3 8 4 16 Q Assume your favorite football team has 2 games left to finish the season The outcome of each game can be win lose or tie The number of possible outcomes is 1 Two 2 Four 3 Six 4 Nine Multiple Step Experiments Bradley Investments can be viewed as a two step experiment It involves two stocks each with a set of experimental outcomes Tree Diagram Markley Oil Stage 1 Collins Mining Stage 2 Experimental Outcomes Gain 10 Gain 10 Gain 5 Gain 5 EvenEven Lose 20 Lose 20 Gain 8 Gain 8 Lose 2 Lose 2 Gain 8 Gain 8 Lose 2 Lose 2 Gain 8 Gain 8 Lose 2 Lose 2 Gain 8 Gain 8 Lose 2 Lose 2 10 8 Gain 18 000 10 2 Gain 8 000 5 8 Gain 13 000 5 2 Gain 3 000 0 8 Gain 8 000 0 2 Lose 2 000 20 8 Lose 12 000 20 2 Lose 22 000 Probability More counting How many ways to get 5 books on a bookshelf Or 5 people in a line Or 5 drivers assigned to 5 busses 5 Of course 5 4 3 2 1 5 Fact 5 Business Information and Analytics Probability Probability Combinations Order does not matter Example 16 teams enter a competition They are divided up into four Pools