P - Probability Module Overview

Probability Module Overview

Introduction

This module is all about probability and how to use probability to make decisions, particularly in a gaming application. We will learn about how to count the different ways of doing things, and then use that to find the probability of particular events happening. Then, we will apply expected value (the average outcome) to casino games and various applications!

Essential Questions

How do I use the General Multiplication Rule to calculate probabilities?
How do I determine when to use a permutation or combination?
How do I graphically display the probability distribution of a random variable?
How do I calculate the expected value of a random variable?
How do I represent and calculate payoff values in a game of chance?
How do I use expected values to make decisions?

Probability Key Terms

The following key terms will help you understand the content in this module.

Conditional Probability - equation image indicator $LaTeX: P\left(A|B\right)=\frac{P\left(A\:and\:B\right)}{P\left(B\right)}$ $P\left(A|B\right)=\frac{P\left(A\:and\:B\right)}{P\left(B\right)}$

Combinations - an arrangement of objects in which order does not matter equation image indicator $LaTeX: _nC_r=\frac{n!}{r!\left(n-r\right)!}$ $_nC_r=\frac{n!}{r!\left(n-r\right)!}$

Empirical Probability - a probability calculated from conducting an experiment

Expected Value - the mean of a random variable X, equation image indicator $LaTeX: E\left(x\right)=\Sigma^n_{i=1}x_i^{ }p_i$ $E\left(x\right)=\Sigma^n_{i=1}x_i^{ }p_i$

Permutations - an ordered arrangement of objects equation image indicator $LaTeX: _nP_r=\frac{n_1}{\left(n-r\right)!}$ $_nP_r=\frac{n_1}{\left(n-r\right)!}$

Sample Space - the set of all possible outcomes

Theoretical Probability - a probability conducted using knowledge of the situation

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