How obvious is dice probability: 

An experiment of probability with two dice

Abstract: 

Dice and probability are deeply related to each other. In this experiment, two six sided dice are being used in order to find out which sum has the highest probability to be rolled. The two dice will be rolled 100 times and the outcomes will be recorded every time in the notebook. The data will later be used to find the highest probability of the sum of two dice to be rolled. My hypothesis is that seven will be the highest rolled sum. However, the experiment says that eight is the highest rolled sum. 

Name: Mymona Tasnim

Date: March 8th, 2023

Introduction:

The dice roll experiment is an experiment consisting of two dice which are being rolled 100 times. The reason for conducting this experiment is to determine which sum has the highest probability. I will record the outcome of these dice every time they are rolled in my notebook. After rolling for 100 times, I calculated the statistics of these sums. My hypothesis is, seven is the highest occurring sum of rolling these two dice. 

Materials: 

• 2 six sided dice
• 1 pen/pencil
• 1 notebook/piece of paper

Method: 

1. Take a piece of paper and a pencil.
2. Create a data table in the paper. The table should have three three columns. Label the first column as “Dice sum”. Label the second column as “Times Rolled (Number)”. Label the third column as “Times Rolled (Tally)”. 
3. Label under the dice sum with values from two through 12.
4. Roll two dice together and sum up the results. 
5. Tally down the results in column three in the designated box. 
6. Repeat steps 4 and 5 for 100 times. 
7. Add all the tally marks in the second column. 
8. After rolling a 100 times, identify which sum occurred the most. 

Results:

After completing the steps we found out that eight is the highest repeated sum after rolling the two dice for a hundred times. The median numbers had a trend of being more frequently rolled. Figure 1 and figure 2 represent the data results from this experiment. 

Figure 1 : Bar graph illustrating the sum results of rolling two dice 100 times

Figure 2 : Pie chart showing the sum results of rolling two dice 100 times

Analysis:

From the experiment, it has been clearly proved that eight is actually the highest rolled sum. I recorded the data in my notebook everytime I rolled the dice. Both figure 1 and figure 2 shows the data that were collected from the experiment. Figure 1 is a bar diagram that shows that eight is the highest rolled sum. The x axis represents the sums that were rolled. On the other hand, the y axis represents the number of times a certain sum was rolled. Again, figure 2 is a pie chart which also clearly shows that eight is the highest rolled sum of the two dice. Figure 2 also provides the percentage of each sum. 

A trend sequence shows that the highest frequencies of being rolled lies in the median value numbers. In an article titled “Investigation of probability distributions using dice rolling simulation” by Lukac Stanislav also shows a similar kind of trend. Figure 7 of that article is a bar diagram which shows that the median value has the highest frequency of sums. (Stanislav, 2010)

My hypothesis was seven will be the highest rolled sum and thus my hypothesis has been proven wrong. I think the reason behind choosing seven is that many people consider seven as their lucky number. However, I do want my peers to re conduct this experiment in order to get the best result. 

Conclusion:

The main purpose of conducting this experiment was to determine which sum of rolling two dice has the highest probability. Initially it was thought that seven is going to be the possible outcome but the experiment proved it wrong. After the experiment it has been concluded that eight is the highest repeated sum after rolling two six sided dice for 100 times. In addition to that, it has been found out that the highest frequency of being rolled is in the median values. I also think that the data in this experiment are reliable as the experiment had a lot of trials. 

References: 

Lukac S, & Engel R. (2010). Investigation of probability distributions using dice rolling simulation, page (30-35)

Appendix:

Dice Sum	Times rolled (numbers)	Times rolled (tally marks)
2	1	|
3	2	||
4	8	||||| |||
5	9	||||| ||||
6	12	||||| ||||| ||
7	14	||||| ||||| ||||
8	19	||||| ||||| ||||| ||||
9	16	||||| ||||| ||||| |
10	10	||||| |||||
11	6	||||| |
12	3	|||