The Odds:

Probabilities of rolling dice

Illustration

This report will talk about the probabilities rolling a pair of dice. The numbers from the two dice will be added to get the sum from each roll and then those numbers will be used to figure out the probability of getting a certain sum.

Luis Hidalgo

October 4, 2023

Abstract

In this experiment I attempt to find the probabilities of rolling dice. In the experiment I rolled a pair of dice 108 times then added the numbers from the two dice to get a sum as well as combining the values/scores from each die to see the minimum and maximum score I could get, the minimum being 2 and and the maximum being 12. After having done that I used the sums and the scores to create a graph in order to find a probability/chance of rolling a certain sum of scores. At the end of the experiment I found that the 2 and 12 had the lowest probability of being rolled while the number with highest probability were 6  and eight initially proving that my hypothesis was partially wrong.

Introduction:

The reason for this experiment is to understand the idea of probability and learn how probability works as well as learn how to make a hypothesis and use an experiment to see whether it’s true, false, or even partially correct or incorrect.

Hypothesis

My hypothesis for this experiment is that 2 and 12 have the lowest probability of being rolled while 7 has the highest probability of being rolled.

Materials and methods:

• Electronic Dice- to find the probability of getting a certain sum 
• Pencil- something write down the data
• Notebook- record the data of each roll
• Calculator- to calculate the results of the data
• Computer- to create a graph to display and analyze the data

Results

The results I recorded from each roll were recorded on a table and then used to create a graph to show the probability of each roll.

Figure 1

              Sum of scores     Number of rolls for each score

2	2
3	8
4	4
5	6
6	20
7	18
8	19
9	14
10	8
11	6
12	3

Figure 2

The Probability of each roll

Analysis

My hypothesis for this experiment is that 2 and 12 have the lowest probability of being rolled while 7 has the highest probability of being rolled and from the data shown on the bar graph it shows that 2 (1.9%) and 12 (2.8%) had lowest probability of all the other the scores, but part of my hypothesis was wrong because also according to  to the of the bar graph 7 did not have the highest probability of being rolled, it was actually 6 (18.5%) that had the highest probability. Also according to a workshop run by a teacher Kyle Mclyntyre the conclusions were similar to my hypothesis I had for my experiment. The conclusions of the workshop said that 2 and 12 had the lowest probability, having a 1/36th or 2.8% chance of being rolled. Also, The conclusions said that 7 had the highest probability with a 1/6th or 16.7% chance of being rolled which is what I hypothesized in my experiment.

Conclusion

In conclusion, the probability of rolling a 2 or 12 is very low with 2 having 1.9% chance of being rolled and 12 having a 2.8% chance of being rolled and the number with highest probability of being rolled is 6 with an 18.5% chance. This Information and recorder data can be used and applied in future experiments by being used as reference to either build on or create a new experiment finding probabilities by creating a hypothesis, recording and analyzing data and using that data to prove whether or not the hypothesis is true. Through this process the person engaging in the experiment will also learn how to experiment and learn how to find probabilities and understand them and how they work.  

References

McIntyre, K. (2022, February 2). Roll the dice: A fun probability experiment for all ages. Medium. https://medium.com/@kylejmcintyre/roll-the-dice-a-fun-probability-experiment-for-all-ages-c949727ffd1b