**How to Win the Lottery**

**Probability of Rolling Two Dice**

**Mohammad Alhusaini**

**Adam Bubrow**

**Writing for Engineering**

**March 12, 2024**

**Abstract**

The goal of this lab report is to determine which number comes up most frequently on a 6-sided die. Because of a statistical formula for replaceable collections of objects, I had originally predicted that 7 would be the most common number. This theory turned out to be true since we had actually shown 7 was the most prevalent number. My hypothesis was confirmed by the mean and median of my data set, therefore even my hypothesis that 7 would be the most common number is correct.

The six-sided die is most likely the most widely used of all the dice kinds that people use to play games and make decisions (typically in the context of gambling). The chance of a fair six-sided die falling on any number between 1 and 6 is even; the total of two dice does not follow the same pattern. We can really estimate the likelihood that the total of two dice will equal a specific number by using some basic math. So, in order to comprehend how these possibilities come to pass, I will be investigating testing this using the scientific method and my computer. When we roll two dice, the number seven should come up the most often as there are the most possible combinations of sides that might add up to that number.

**Materials**

- Computer
- Python Compiler
- Google Doc

**Method**

- Open Matlab
- Write a code that chooses a random number between 1 an 12 twice and displays the sum n times, with n being some multiple of 100.
- Write a following scripts that displays the frequency of each sum

**Results**

** ***Figure 1: Bar graph of total sums*

We see that the rolls resemble a bell shape. The figure shown shows that the frequency of the rolls of 6 and 8 was the same. Mathematical examination of this data reveals that the data set’s mean and median are, respectively, 7.24 and 7.

**Analysis**

** **My hypothesis has been validated based on the data gathered from the experiment, which shows that the most often occurring number is 7. My prediction was confirmed by the data, which show that the mode and median are both exactly seven, the number that was predicted. My idea was thus confirmed by the experiment.In a similar vein, Peter K Dunn Department of Mathematics and Computing, University of Southern Queensland, Toowoomba, Australia refuted the experiment in which he examined the likelihood that the total of different six-sided dice would equal six. In his experiment, he discovered that if multiple dice were thrown that number would increase exponentially and the common number thrown would be a 8.

**Conclusion**

We were able to ascertain from our experiment that our results correspond with the figure we had computed and our initial hypothesis. As a result, we may now use the knowledge we have found as a set provided to investigate more intricate statistical and probabilistic problems, such as the outcomes of the lottery or the ball landing on black in a casino.

**Citations:**

- Dunn, P. K. (2005). We can still learn about probability by rolling dice and tossing coins. Teaching Statistics, 27(2), 37–41. https://doi.org/10.1111/j.1467-9639.2005.00205.x