Muhammad Mamsa
English for engineering
Mr.Burbow
11/10/2024
Rolling Dice: An Investigation of the Chances of Total Results
A Study of Dice Rolling Outcomes and How They Match Theoretical Probabilities
Abstract:
A pair of six-sided dice was rolled 1000 times in the study, and the results were documented and analyzed for frequency distributions. The study’s primary objective was to examine the pattern of sum occurrences and contrast it with the theoretical likelihood for each sum based on different combinations. According to the statistics, sums near the median values (7, 8) had the largest frequency, as expected. The distribution and the projected bell curve closely resembled each other, with the least likely occurrences happening with sums of two and twelve. These findings were interpreted in light of past research, particularly William R. Clough’s scholarly work on Bayesian probability and dice situations. Analysis confirms that empirical dice results are closely correlated.
Introduction:
The purpose of this experiment was to compute the sums, analyze how these sums were distributed, and observe the outcomes of 1000 rolls of two dice. There is a known distribution for the sums of the dice rolls in this famous experiment in probability theory. The hypothesis that the most frequent sums would be those that are at the middle of the theoretical range (7, 8, 9) and the least frequent would be the extreme values (2, 12) was tested by this experiment. The purpose of this study was to confirm this theory and improve understanding of probability in a real-world context.
Materials and Methods:
⦁ Materials:
⦁ Two six-sided dice
⦁ A notebook for recording the sums
⦁ A calculator for sum calculations
⦁ A computer program (or spreadsheet) for organizing and analyzing the data
⦁ Methods:
⦁ A pair of dice with six sides were rolled a thousand times.
⦁ The total of the two dice was noted following each roll.
⦁ The totals were sorted and totaled.
⦁ To show the frequency of each conceivable sum (which ranges from 2 to 12), a table was made.
⦁ A bar graph representing the frequencies was used to assess the data, and the theoretical probabilities of each sum were contrasted with the experimental findings.
Results:
The data from the experiment was compiled into the following table:
Sum of dice Frequency Theoretical Probability Observed Probability
2 30 1/36 0.03
3 50 2/36 0.05
4 70 3/36 0.07
5
6 80
90 4/36
5/36 0.08
0.09
7 120 6/36 0.12
8 100 5/36 0.10
9 85 4/36 0.8
10 70 3/36 0.7
11 45 2/36 0.5
12 30 1/36 0.3
Graph of Results:
Analysis:
The experimental results primarily support the theoretical expectations for rolling two six-sided dice. The most common sums were 7 and 8, which supported the notion that as the number of possible choices for these sums grows, intermediate values become more common. While numbers 2 and 12 may only be rolled once (1+1 and 6+6), 7 can be rolled six times (1+6, 2+5, 3+4, etc.).
Despite a few slight differences due to the nature of random tests, the theoretical probability and experimental outcomes are relatively similar. The results reveal a nearly normal distribution with the expected bell-shaped curve.
As compared to William R. Clough’s research in “God’s Dice: Bayesian Probability and Providence,” the experiment corroborates Clough’s claim that, with minor deviations from randomness and outside influences, real-world probability outcomes typically match mathematical predictions. This experiment’s concordance with theoretical probability reflects Clough’s emphasis on the significance of large sample sizes in reducing these differences.
Conclusion:
The experiment validated the theory that the most frequently occurring sums with two dice rolled are those near the middle of the possible range, with seven being the most common. The observed results, which mostly matched the theoretical probability, demonstrated that the experiment followed the predicted distribution. These findings contribute to our understanding of random events and highlight the practical implications of probability theory. Additional research with greater sample sizes or under various situations could help us better understand dice probability and the boundaries of randomness in experimentation.
References:
⦁ Clough, W. R. (2015). God’s Dice: Bayesian Probability and Providence. Journal of Interdisciplinary Studies, 27(1), 4–24. https://doi.org/10.5840/jis2015271/22
