Lab Report

Three is the Number: Dice Rolling Experiment.

Nadia Nuru

10/23/19

 

Abstract : Probability is a theory which is based on an analysis of a random phenomena. “The  outcome of a random event can be determined before it occurs, but it may result in any of the possible outcomes” stated by  David O. Siegmund who is a statistic professor at Stanford University.Dice rolls is one common way in which probability occurs in. Dice rolling allows getting a set of number which is based used probability. This experiment consists of a pair of dice being rolled 100 times and recording the sum of the two dice for each roll. After rolling and recording the outcomes for 100 times, I determined which sum had the highest probability of being rolled. 

 

Introduction: The dice rolling experiment is composed of rolling a pair of dice 100 times. The purpose of conducting this particular experiment is to see which sum of two dice being rolled will have the highest probability of rolls. The experiment also proves the theory of probability because a dice have six sides, which means that there will be six different effects to be observed for every sequence in this experiment. Each time the dice is rolled, data of the sum of the number will be collected. After gathering all of the data, I calculated the stats of the sums. My hypothesis is that three will be the highest frequent sum from the two dice that are being rolled. 

Materials:

2 dice 

Paper

Pencil 

Ruler

 

Methods: 

1. I started of by using a piece of paper, pencil and a ruler to draw a table with three columns and three rolls. 
2. I labeled the table that I made with important facts such as “dice sum”, “number of times rolled” and “times rolled”. 
3. I rolled a pair of dice, added up both of their sum and recorded the sum I got from both of their sum.
4. I tallied the number of times I got that sum that was rolled.
5. I repeated procedures three and four for 100 dice rolls.
6. Collected data from all 100 rolls and made calculations of which number appeared the most.
7. Proved my hypothesis based on the results.

 

Results: After completing the experiment, the results shows that 5 is the most frequently rolled sum from the pair of dice. Shown below, Figure 1 is a table which displays the data from the results and Figure 2 is a bar graph that shows data from the results of the experiment representing the 100 rolls and their rolled. 

 

Figure 1 : Table that shows 100 rolls and their rolled number tallied.

 

Dice Sum	Number of times it occurred when Rolled	Tally of times rolled
2	7	IIIIIII
3	12	IIIIIIIIIIII
4	5	IIIII
5	20	IIIIIIIIIIIIIIIIIIII
6	6	IIIIII
7	8	IIIIIIII
8	17	IIIIIIIIIIIIIIIII
9	5	IIIII
10	8	IIIIIIII
11	1	I
12	11	IIIIIIIIIIII

 

Figure 2 : Bar graph displaying 100 rolls and their rolled number.

Analysis: After establishing the dice roll experiment, results displayed that the most probable sum after rolling a pair of dice 100 times was Five. Every time the dice were rolled the sum of the roll were jotted down. Figure 1 and figure 2 both revealed the data from the rolls. Collecting  data from all 100 chances allowed the experimentation to be precisely noted. From my experiment, the greatest amount was five which occurred 20 times. Shown below, figure 1 and figure 2 proves that 5 was the most probable and 8 was the second most probable and 3 was the third highest with the number of 12 as the most time it appeared. Going back to my hypothesis, I can witness  that my hypothesis was incorrect because I stated that the number three would be the highest rolled sum but it was five instead. The reason for my hypothesis choosing three as the number most frequently rolled sum is because I thought three might be the number since in most dice games many people say seven is a lucky number but I knew it will be something odd and otherwise so I thought of three. A study that was familiar to this experiment was the “The probability distribution of the sum of several dice: Slot Applications.” The authors of this study were Singh, Ashok K, Dalpatadu, Rohan J. and Lucas, Anthony F. In this study, the moment generating function strategy was used to develop the probability of the sum of K dices. K represents the sum of the dice. They used a function in solving the probability of which sum of numbers will appear frequently. Seven was the number that was derived the most from all 36 trails. This study shows that there are many ways in which we can find the statistics of probabilities. 

 

Conclusion: The objective of this entire experiment  was to figure out the most possible sum after rolling a pair 100 times. My hypothesis was that the number three would be the most frequently rolled number, however from the experiment one can conclude that five is the most probable number. Creating  this experiment conveys that probabilities are always random and it changes anytime. Probability can not be accurately determined. The data collected from this experiment is very reliable because of the amount of trails I used which prevented any sort of mistakes.

 

Work Site

https://www.britannica.com/science/probability-theory

https://digitalscholarship.unlv.edu/cgi/viewcontent.cgi?article=1025&context=grrj

Singh, Ashok, et al. “The Probability Distribution of the Sum of Several Dice: Slot Applications.” UNLV Gaming Research & Review Journal, vol. 15, no. 2, 2011, pp. 109–118.