Rolling for a Chance:

Studying the Probability of Dice

In this experiment we explore why a pair of dice is a good way to explain probability. We roll a pair of dice 100 times to determine the probability of dice. We use this method to explain why eight is the number that has the highest probability to be rolled compared to all other numbers.

Introduction

Probability is the likelihood of something happening or being the case. This case of probability is seen everywhere in the world. We see it in things such as how many times a person will make a basketball shot in, or how often will a train be on time. These cases of probability determine the ratio of something will or won’t occur in their given scenario.

These scenarios seem almost random at first glance. However, what if there was a way to determine the probability of something occuring. In the scholarly article “Roll THE DICE — an introduction to Probability” it states that, “ This dice game also helps to explain the benefits of using a large sample rather than a small one. The game is constructed to seem fair – it appears that each student has an equally likely chance of winning – but it is decidedly unfair.” This “dice game” is the entire premise of the experiment performed today. A pair of dice will be rolled 100 times to see what number will be rolled the most. I determine that nine will be the most rolled number because of how close both numbers are to one another on a die.

Methods and Materials

For this experiment, the use of an online dice rolling website dice.virtuworld.net instead of an actual pair of dice to recreate the dice roll for the sake of convenience. This will allow the experiment to be more accurate as human error will not be present during the actual rolling of the dice. Once on the website set the number of dice to 2 as the experiment will only be using a pair of dice, and the amount of sides to the standard 6 sides. Once the pair of dice is rolled, record the number and repeat the process 100 times.

Results

After completing a 100 rolls of a pair of dice, the amount of a certain number on a pair of dice was recorded. The highest number rolled over a period of a 100 times was eight with 17 rolls. The lowest being two with only 4 rolls. One was never even an option as a pair of dice can never equal only one, and the rest of the numbers all ranged from 4-17 as shown in figure 1.

Figure 1

The percentage of times eight was rolled was 17%. This percentage was calculated out of the 100 times the pair of dice was rolled. Two also being the lowest percent with only 4% out of 100 times the pair of dice was rolled. This is shown in figure 2.

Figure 2

Analysis

After 100 rolls the number eight had the most rolls out of any other number rolled. This means that seven has the highest probability over every other combination of numbers thrown using a pair of dice. Eight has many possible combinations that can combine into one another to equals it. The pair of two and six, or four and four are examples of these such combinations.

Compared to my hypothesis that nine would be the number with the highest amount of rolls, it is very similar to why the original hypothesis was created. Both numbers have multiple ways of combining two dice to equal them. And the numbers to make them are very easy to roll making them an easy guess to choose on which number would have the highest probability.

This study is very similar to the one used by Ray Huntley’s article “Sport versus Probability: Dice Simulation of Australian Rules Football,” a similar study used dice to help determine the probability of Australian Football. This method made it simpler to determine how often a goal would score in a quarter. The use of dice makes probability in terms of numbers and creates an easy way to interpret the data.

Conclusion

Eight being rolled the most after 100 attempts of rolling a pair of dice, proves that it has the highest probability. It has the highest chance of being rolled compared to any other sum of the other dice rolls. Probability is not limited to just dice, it can be seen all over the world and in our daily lives. You just have to think a bit and you’ll realize how much of the world is let up to chance.

Work Cited

FREDA, A. (1998). Roll THE DICE — an introduction to Probability. Mathematics Teaching in the Middle School, 4(2), 85-89. Retrieved from http://www.jstor.org/stable/41180487

Huntley, R. (2008). Sport versus Probability: Dice Simulation of Australian Rules Football. Mathematics in School, 37(4), 28-30. Retrieved from http://www.jstor.org/stable/30216501