Abstract:
We’ve all rolled dice at least ones in our lives. In this experiment I’ll be doing just that except 100 times with a pair of dice instead of once. Each dice is 6 sided. Per roll I will be calculating the sum and using the data collected to figure out which sum had the highest probability of being rolled. My hypothesis is that the number 8 will be the most frequently rolled sum. According to the data I collected my hypothesis was correct. The sum of 8 had a 21% chance of being rolled compared to other sums.
Introduction: In this experiment we will be challenging dice probability. The experiment itself consists of rolling a pair of dice 100 times and recording the sum for each roll. The pair of dice will each have 6 sides which means that the minimum sum we can get is 2 and the maximum is 12. Since there’s 6 sides on each dice there are 36 different arrangement of numbers and 11 possible sums. My hypothesis is that the sum with the highest probability of occurring will be 8.
Materials:
- Pair of Dice
- Sheet of paper
- One pencil
Method:
- Start by rolling the pair of dice and calculating the sum.
- Once you have the sum record it onto your sheet of paper.
- Repeat the first two steps 100 times.
- Once you’re done, look at which sum occurred the most.
Results:
After completing the experiment, results showed that eight was the most frequently rolled sum. Looking at Figure 1 we can see that sum 6-8 had the highest chance of being rolled. Figure two clearly shows the percentage of the sums 1-12.
Figure 1: Bar graph representing how many times each sum was rolled out of the 100 rolls.
Figure 2: Pie Chart representing the sums in Percentages.
Analysis:
After completing our experiment, results showed that out of a 100 dice rolls the sum of 8 reoccurred 21 times. After each roll the sum was calculated. Once I was done with collecting the sums for all the rolls and the data collected was used to create a bar graph (figure 1). The bar graph was then converted into a pie chart that shows the percentage of each sum occurring after the 100 rolls (figure 2). When we look at figure 2, we can clearly see that 8 was the most common sum that was rolled. 1,2, and 3 were the least common sums rolled. My original hypothesis was that the most common sum would be 8, which was correct. The reason why was because with a pair of dice there’s 3 possible ways of getting 8 as a sum.
One study called, “Probability Experiments with Shared Spreadsheets” by Darin Beigie conducts a similar experiment with dice. However, the results concluded that the most frequent sum was 7 instead of 8. The reasoning for this was because the sum 7 had “the most possible combinations of numbers on the two dice” (Beigie 486). Beigie also found out that the least frequent sums were 2 and 12 because they only had one possible way of getting those sums (1+1 or 6+6). Overall both of our results are due to the fact that median sums like 7 and 8 have more than one possible way of getting them.
Conclusion:
In the end we have gathered enough data to conclude the experiment. Through the experiment we’ve been able to identify the sum that frequently occurs when a pair of dice is rolled. Our hypothesis was that the number eight would occur the most. Which in the end was true. This is because out of all the 11 possible sums, 8 had three possible ways of occurring (2+6, 5+3, 4+4). Since we rolled the pair of dice 100 times, we don’t have to worry about our data being caused by chance. In the end the more dice rolls you do the more accurate your experiment will be!
Works Cited:
Beigie, D., Johnson, G., & Dogbey, J. (2010). mathematical explorations: Probability Experiments with Shared Spreadsheets. Mathematics Teaching in the Middle School, 15(8), 486–491. http://www.jstor.org/stable/41183523
