Module 04 Assignment – Applying Game Theory
Overview
Gaming and probability are intertwined. In fact, there is an entire discipline in mathematics called “Game Theory.” In this assessment, you will apply discrete and continuous probability distributions to games. There will be two parts: the first will concentrate on discrete probability distributions, and the second part will focus on continuous probability distributions.
Instructions
Part One – Data Table
The theoretical probability of rolling a fair six-sided die is 1/6 for any specific single outcome, such as rolling a one. You want to test the theoretical probability by running an experiment.
In this experiment, you need to roll a six-sided die 25 times. Record the outcome of each die roll. Create a discrete probability distribution using your outcomes as the probability. For example, if you rolled 4 fives out of your 25 total rolls, your probability would be 4/25.
x 1 2 3 4 5 6
P(x)
Part Two – Discrete Probability Distribution
After filling in the table above with your experimental probability, answer the following questions. Show all work for full credit. Calculations should be performed in Excel while answers including an explanation of steps using proper terminology are provided in a separate document.
1. What is the expected outcome for rolling a six-sided die using the discrete probability distribution table above?
2. What is the probability of rolling an even number according to the discrete probability distribution table above?
• How does this compare to the theoretical probability of 0.5?
• Explain why you think there is a difference between the theoretical probability and the experimental probability you found.
