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# Appendix 3: Basic Probability Concepts

## INTRODUCTION

Probability is the language of risk and uncertainty. Since risk and uncertainty are essential elements of business life, a basic understanding of this language is essential for the business analyst. In this appendix, we present some of the elements of probability as they are used in business modeling. We focus on knowledge that an analyst might want to draw on during a model-building project. We begin by describing probability distributions for uncertain parameters; then we discuss expected values, variances, and tail probabilities, describing why they are generally appropriate measures for decision making. Finally, we describe the elements of sampling theory in order to provide the background for the text's coverage of data analysis and simulation.

## PROBABILITY DISTRIBUTIONS

For any parameter in a model, we should give some thought to the precision associated with its value. Very few parameters are known for certain, especially in models that predict the future. In various chapters of the book, we discuss ways to take this uncertainty into account. The simplest approach is sensitivity analysis, in which we vary one or more parameters to determine how sensitive the model results are to changes in the parameter values. For example, we might determine that if sales are high next year (50 percent above this year's level), our profits will be \$5 million, whereas if sales are low (25 percent below this year's level), our profits will ...

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