# MDM4U CULMINATING PROJECT – PROBABILITY

Your task is to create a probability-based game that can be played purely on chance. Your game may involve dice, cards, coins, spinners, etc. However, it MUST have at least 3 events in each trial. For example, rolling a die 3 times. You may also choose to create a game involving poker hands, or blackjack hands, but you should check with Mr. Leung first once you have an idea.

Brainstorm the instructions for your game

Decide on the appropriate payout structure for the winners

Test your game out to make sure it makes sense and is completely a game of chance Determine the theoretical probability calculations, expected values, and the expected payout Determine the experimental probability based on at least 100 trials (you may conduct this by hand or using simulation software)

Determine the expected payout

Analyze the theoretical probability of a player winning at least 3 out of 5 games if they chose the option that has the greatest chance of winning

Conclusions

Create a well-organized final report

MDM4U1 Data Management Culminating Project PROJECT COMPONENTS

COMPONENT #1 GAME DESCRIPTION (10 MARKS)

Clearly state your:

Games name

Description of game and relevant background information

Outline of the rules, including how to win

Explanation of the fee structure (cost to play)

Summary of the payout structure for every possible outcome

Notes:

Organize numerical values in charts and tables

COMPONENT #2 THEORETICAL PROBABILITY (25 MARKS) Introduction

o One paragraph. Explain what you are going to show in this section

Theoretical Distribution with Observations/Analysis/Explanations

o Possible Outcomes

o Probability Distribution

o Expected Payout

Conclusions what have you learned so far?

o Conclusions are very important! What does this tell us about your game? Is your game a fair game? Justify your answers with reference to your numerical statistics and graphs. Use full sentences and proper paragraphs.

COMPONENT #3 EXPERIMENTAL PROBABILITY (15 MARKS) Introduction

o One paragraph. Explain what you are going to show in this section.

Experimental Data First 10 trials ONLY (you have to do 100 +)

o Outcome chosen, Actual result, Win/Loss, Payout to player, Payout to House

Experimental Distribution with Observations/Analysis/Explanations

o Possible Outcomes

o Probabilities

o Total Payout and payout per trial

Conclusions what have you learned so far?

o Conclusions are very important! What does this tell us about your game? Is your game a fair game? Justify your answers with reference to your numerical statistics and graphs. Use full sentences and proper paragraphs.

MDM4U1 Data Management Culminating Project COMPONENT #4 PROBABILITY ANALYSIS (6 MARKS)

Introduction you overhear a student saying This game is so easy. I could win more than half the times I play. Introduce this section as your proof as to whether their statement is correct or not.

Probability Analysis question, calculations & conclusions

o Probability Distribution question (include a graph or table). What is the probability of a person winning in at least 3 out of 5 consecutive games, assuming they choose the outcome with the highest theoretical probability of success?

Probability conclusions

COMPONENT #5 CONCLUSIONS (4 MARKS) Summarize your conclusions.

o Is this game a good game for the person running it? For the person playing? Would you play this game?

o Make conclusions based on your observations. Use full sentences and proper paragraphs.

FINAL REPORT (60 MARKS TOTAL)

Your final report should consist of the following sections.

Title Page Include your name, topic, course, teacher, date

Table of Contents Most word processors can create this automatically if you use built in headings

Game Description

Theoretical Probability

Experimental Probability

Probability Analysis

Conclusions