Finding the Same Dice Based on Probability?
Mohammed Hossain
CCNY- CUNY
Writing for Engineering, Fall 2019

Abstract :
In this lab, the probability is measured and recorded via the usage of dice, which have varying numbers of dots. When rolled, they can display different combinations due to the cube having certain numbers of dots on each respective side. Also, a random variable assigns a unique number to each event from a sample space. In experiment simply records the tossing of a dice one-hundred times. The main goal is to measure if any same frequencies are recorded or depicted by the results. In total there are thirty-six combinations that can be found from the dice probability experiment. Probability shockingly has its own formula which can be seen as, (# of expected outcomes/ # of attainable outcomes). The primary focus is to measure the results after one-hundred rolls.

Introduction:
The main goal of this experiment is to show what probability is, and how it works. Probability is not just a simple term, it is best defined as the chance of something occurring. In this case, the amount of times certain combinations are landed upon is what will be measured. The experiment depicts the likelihood of certain combinations, as well as the unlikelihood of other combinations; as a visual will be provided along with the actual rolling of the dice pieces. Since there are thirty-six combinations possible, two dice, and formulas that may be utilized depending on the circumstances there will be differing results provided for each trial produced. To be more specific, throughout this experiment it was pondered as to how many times it will take the dice to be rolled to attain the same number. The estimate was possibly around twenty times at most throughout various trials. Since there are six sides to the die, then there will be six outcomes that can be worked with and combined with the addition of the ther die. A generator was used to help make this experiment happened, where the range of one to six was used to generate the results (which would happen at a random) . In the end it was then determined how many times it took to get the same numbers in the dice, ironically certain dice sides did appear more than others in the differing trials despite not being a thought out addition to this experiment.

Materials:
Online Dice Generator
Charts/tables
Dice (optional if opting for actual dice usage)
Pencil
Recording book
Calculator (optional)
Method:
To attain solid results, the software was used to generate the dice rolls at an interval of one-hundred. These results were displayed randomly, there was no specific measurements to this, and this was done three times to record any differences. At each trial the results were recorded, in total three were done. Once pairs were counted for the dice, an average was taken of all trials; which was simply a sum of all the trials divided by three. This was then noted as the final number of times it took for the dice to land on the same number together. This as further set up mathematically for anyone to follow, as well as recorded in a chart to display results.

Results:

Three Experimental Trials for the Dice:

Trials:
The number of Times Same Pairs Were Landed Upon:
1
14 times
2
14 times
3
15 times
Average :
14 times approx

Calculating the average :

(14+14+15)/3= 14.33 approx

Rounded version: 14 times approx

Analysis :

These results were perhaps, close to what was expected but not quite as well. In totality only around fourteen percent of the time did the dice land in pairs. This number was no largely off from the work exhibited by an elementary school child. Rather this child rolled forty dice at a time to record if the same numbers would be received, this was done in five trials. The experiment utilized in this case was with to dice pieces, and rolling them a hundred times in three total trials. The major note from this child’s experiment was that all numbers were in the range between fifteen to seventeen; with the outlier of twenty in the final trial. In the three trials done in regards to rolling the dice one-hundred times, it was important to pay attention to how the range was not completely off when compared to the experiment done by the child.
The range for this experiment was between fourteen to fifteen. However, the average for the experiments did differ. Since there was a large sample size to work within the child’s experiment their average was 16.6 or 17 when rounded, this indicated that the dice were the same based on this numerical average. On the contrary, in my own experiment, the dice were the same around 14.3 times or 14 when rounded in total. The leading analysis from both situations was that when there is a larger sample size to work with, like forty dice as the child used and differing trials (rather than a standard three trial experiment), one is more likely to see dice pairs appear more than expected. My own experiment used standard scientific measures, such as the three trials and usage of two dies as suggested.
Based on all these results, it can be easily understood that when larger amounts of a die are used there are the possibilities for more similarities to be noted. However, in the case of limitations like in my own experiment; the similarities are likely to be settled down to the bare minimum of results. In the final trial for the child, there were twenty of the same die exhibited; and throughout there were slight increases. My experiment stayed relative to its measures ironically.

Conclusion:
In summary, the initial hypothesis was incorrect. There were not twenty dice pairings that were the same from the sample size used, rather it was 14.3 or 14 to be more precise in this case. The reason being for this was likely due to the amount of die used and of course how many times they were rolled. The basic three trials yielded a number that was off slightly but to further verify if this was correct or not another experiment was used. This time a child had forty dies and rolled them as many times as possible in the five trials to get the totality of how many times these die pieces were the same. Since there were five trials, a number that was not set for the number of rolls, and finally forty die utilized major conclusions were drawn.
It seemed as though when the larger sample size was used, and the experiment was broadened in terms of the number of materials used and the amount of time utilized; the number of times the dice pieces were the same increased. Since there are more pieces to play around with as the child did in their experiment, results, and ranges will be increased. In my own experiment, during these three trials, everything mostly stayed at fourteen but one trial, which went up to fifteen. With a wider variety of numerical values, there is the likelihood of seeing how many times these dice can have some of the same pairings. In the near future, it would be suggested that more trials are used in accordance with the two dies; as well as varying trials with more than two die. Overall, larger sample sizes yielded larger values in regards to the dice being the same– however smaller sample sizes yielded smaller values.

Works Cited:
Edkins, J. (n.d.). Throwing dice – theory. Retrieved October 19, 2019, from http://www.gwydir.demon.co.uk/jo/probability/calcdice.htm.
Holmes, S. (2000, November 28). Probabilities for the two dice. Retrieved October 21, 2019, from http://statweb.stanford.edu/~susan/courses/s60/split/node65.html.
Kearney, V. (2017, February 6). Science Fair: Rolling Dice Probability Experiment. Retrieved October 20, 2019, from https://owlcation.com/academia/Science-Fair-Rolling-Dice-Experiment.