# Applications of Calculus in Geometrical Probability (UMAP)

### Author: Richard M. Dahlke and Robert Fakler

The geometrical probability model is defined in this module, and examples of probability problems are given in which considerable thought is required in translating the problems into mathematical models. Once models are constructed, probabilities are derived by using various methods for calculating areas or volumes of the sample space and success region, using single or double integration. A computer simulation of a probability problem is motivated, defined, and used to solve probability problems already solved using analytical techniques. Exercises are given after each of the three major sections of the unit.** Table of Contents:INTRODUCTION** What is Geometrical Probability?

Why Study It?

**GEOMETRICAL PROBABILITY MODEL**

Geometrical Probability Model

Determind Probability Bounds

**APPLICATIONS**

Functions of One Variable (Single Integration)

Exercises

Functions of Two Variables (Double Integration)

Exercises

**SIMULATION**

Real-World Simulation

Computer Simulation

Exercises

**SAMPLE EXAM**

ANSWERS TO EXERCISES

ANSWERS TO SAMPLE EXAM

ABOUT THE AUTHORS

ANSWERS TO EXERCISES

ANSWERS TO SAMPLE EXAM

ABOUT THE AUTHORS

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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