Rolling into Statistics 

The sum of 100 dice rolls 

Abstract: 

In this lab report, the probability distribution of rolling a pair of dice is analyzed by conducting 100 rolls. Each roll of the pair of dice can result in sums ranging from 2 to 12, with varying possible outcomes. The experimental results, as depicted in the attached screenshot, show that the sums 5, 6, and 7 occurred most frequently, with 12, 16, and 21 occurrences respectively. Notably, the sum of 7 had the highest frequency at 21%, aligning with theoretical probability expectations. The sums at the extremes, such as 2 and 12, occurred least frequently, each appearing only once and five times respectively. This is because there is only one combination to achieve these numbers which lessens the chance of us rolling these numbers. This experiment demonstrates the practical application of probability theory in predicting outcomes of random events, with the results closely matching expected distributions. 

Engineering for Writing 

Kareem Alchorbaji 

Maruf Khan 

March 12, 2025 

Introduction: 

Have you ever wondered why rolling a 7 feels so common in dice games? Why is it 7 and not any other number? In this experiment, we dive into the fascinating world of probability by rolling a pair of dice 100 times to uncover which sums appear most frequently. The goal is to understand how chance influences outcomes in games like Monopoly or Craps and to see if real-world results match what probability theory predicts. In theory the number that has the greatest number of ways to be formed through the adding of both dice should be the number that would be rolled the most. Which is why we expect that the sum of 7 will stand out as the most frequent result as it has the highest number of combinations (six possible ways) compared to other sums. By analyzing the data, we’ll gain valuable insights into why certain numbers are more likely to appear and how this knowledge can be applied to games and decision-making. Let’s roll the dice and see what the numbers reveal! 

Materials and Method: 

Materials: 

• Computer: A device capable of running Python code. 

• Python Programming Environment: Software like Python IDLE, Jupyter Notebook, or any IDE that supports Python.  

• Random Module: A built-in Python library used to simulate random dice rolls. 

Method: 

• Code Setup: A Python script was written to simulate rolling two dice 100 times. The script uses the random module to generate random numbers between 1 and 6 for each die. 

• Simulating Dice Rolls: The roll_dice function initializes a dictionary to store the frequency of each sum (2 to 12). It then rolls the dice 100 times, calculates the sum of each roll, and updates the frequency in the dictionary. 

• Displaying Results: The display_results function prints the results in a table format, showing the sum, frequency, and percentage of occurrence for each possible sum. 

• Execution: The script is executed by calling the main() function, which performs the dice rolls and displays the results. 

Result: 

Fig. 1- Python code: Sum of 100 dice rolls  

Fig. 2- The chance a number combination is rolled 

Fig 3. Percent of Probability of a role  

Analysis: 

The results of the dice-rolling experiment, as shown in the attached image, align closely with the theoretical probabilities of rolling two six-sided dice. The sum of 7 occurred most frequently, appearing 21 times (21%), which matches the expected probability of 16.67%. This is because there are six possible combinations (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) that result in a sum of 7, making it the most likely outcome. Sums like 2 and 12, which have only one possible combination each, appeared the least frequently (1 and 5 times, respectively). The results for other sums, such as 5, 6, 8, 9, 10, and 11, also followed the expected trend, with frequencies decreasing as the number of possible combinations decreased. 

Fig 4. Total sum and possible rolls to achieve that sum 

Comparison to Another Study 

In another similar experiment, researchers conducted an experiment with three dice instead of two. They found that the sums 9 and 10 occurred most frequently, and 10 was more likely than 9. This was because there were more possible combinations to have a sum of 10 than that of 9, as illustrated in Figure 5. (Lukac, Stanislav, and Radovan Engel. (vol. 66, no. 2, 2010, p. 30+) “Investigation of probability) 

Fig 5. 

Conclusion 

The experiment successfully demonstrated how the probability of each sum when rolling two dice can be calculated through the use of random probability. This was done through the use of a code that allowed 100 roles to be done with 2 dice that had 6 faces, in which the data collected from the 100 rolls was used to calculate the percent of a certain number being the most frequent. Our theory was proven to be correct as it makes sense that the number that has the most combinations would be the number that would be rolled the most. In this case the number was 7 due to it having 6 different combinations and not numbers like 2 and 12 as they have the least combinations. Experiments that have more rolls would be more accurate for future references. Also, human interaction can also mess up the outcome of the dice rolls since using our hands like in a board game would slightly affect the odds.  

Works Cited 

Dice. (n.d.). Retrieved from http://mathworld.wolfram.com/Dice.html 

Lukac, Stanislav, and Radovan Engel. (vol. 66, no. 2, 2010, p. 30+) “Investigation of probability 

 distributions using dice rolling simulation.” Australian Mathematics Teacher. Academic OneFile, https://link.galegroup.com/apps/doc/A229718040/AONE?u=cuny_ccny&sid=AONE&xid=27cfcf59.