Being able to process, organize, and collect data are mathematical ideas that are important to use when solving probability problems. These concepts helped me easily solve two problems assigned in class. The first problem is called Paula’s Pizza. It stated that a woman named Paula ordered a two topping pizza, but the server only wrote down that Paula wanted a two topping pizza--how would the chef know what two toppings Paula wanted? There are 6 different toppings, and it was our job to figure out the probably of Paula getting the pizza she wanted. I started by processing the data. I used a tree graph to write down every combination of toppings Paula could get, then eliminated any doubles or repeat combinations. It also helped organized the data and kept me from getting overwhelmed by numbers. By doing this I figured out that there were 15 different pizza combinations that Paula could have gotten. This helped me learn about probability because it was a simple introduction on how to solve probability problems. At the end, I figured out there was a 1/15 chance she will get the pizza she asked for and a 14/15 chance she will get a pizza she does not want. The other problem is called Rug Games, this is very different from Paula’s Pizza problem, but the same process can be used to solve it. For the Rug Problem, we had to figure out the probability of a dart falling on a certain part of a rug. Each rug had two to three colors, and we had to find a way to predict where the dart was most likely to land. I approached this problem by dividing the rug into separate but equal sections and counting how many sections of each color there were. Then, I set up the probability equation for each number and compared the answers to figure out which color was most likely. These problems were two different but equally important ideas that helped affect my behavior in situations that involve probability. Each one showed me a different way to approach probability questions and they both helped me to further understand the subject.

I am most proud of my work in the Counter Game because I was able to use probability to win the game every time. For the Counter Game, I had to put markers on a strip of numbers labeled 2-12. The point of the game is to roll two dice a remove a marker on the number that corresponds to the sum of the dice. The strategy I came up with was to find the probability of the dice equaling each number and put the most amount of markers of the most likely numbers. By using this strategy, I was able to win two out of three time, and the last time, I was only one away from winning. This problem helped me further understand how probability can be used in the real world. I was able to win by using simple mathematical ideas, which I continue to use to my advantage in the future.

Two Habits of a Mathematician I used in this project were Solve A Simpler Problem and Be Confident, Patient, and Persistent. I used Solve A Simpler Problem in the Rug Problem by taking each section apart and first solving each section instead of trying to just jump in and figure out the final answer. With probability problems, there often many small problems that need to be solved before the final answer can be found. By starting small and finding a simpler problem, I could tackle the work that I had quickly and without getting confused. I think I grew by using this habit because it helped me solve the problem, and by practicing it, it can continue to help me with problems in the future. I used the habit of being Confident, Patient, and Persistent in Paula’s Pizza because this problem had a lot of different parts and it was quite confusing at times. The first time I did the problem, I did it wrong. I calculated the number of pizza combinations Paula could have gotten incorrectly, I forgot to eliminate the doubles and I came out with a number of combinations that was much bigger that the actual number. But, I was patient and persistent with my work and was able to re-do the problem so that I could find the correct answer. After I re-did the problem, I was more careful and finished the problem easily. This habit will helped me grow because it helped remind me to be cautious and double check my answers. I will be able to use this habit in the real world because it is a skill that could prevent me from making similar mistakes again.

I am most proud of my work in the Counter Game because I was able to use probability to win the game every time. For the Counter Game, I had to put markers on a strip of numbers labeled 2-12. The point of the game is to roll two dice a remove a marker on the number that corresponds to the sum of the dice. The strategy I came up with was to find the probability of the dice equaling each number and put the most amount of markers of the most likely numbers. By using this strategy, I was able to win two out of three time, and the last time, I was only one away from winning. This problem helped me further understand how probability can be used in the real world. I was able to win by using simple mathematical ideas, which I continue to use to my advantage in the future.

Two Habits of a Mathematician I used in this project were Solve A Simpler Problem and Be Confident, Patient, and Persistent. I used Solve A Simpler Problem in the Rug Problem by taking each section apart and first solving each section instead of trying to just jump in and figure out the final answer. With probability problems, there often many small problems that need to be solved before the final answer can be found. By starting small and finding a simpler problem, I could tackle the work that I had quickly and without getting confused. I think I grew by using this habit because it helped me solve the problem, and by practicing it, it can continue to help me with problems in the future. I used the habit of being Confident, Patient, and Persistent in Paula’s Pizza because this problem had a lot of different parts and it was quite confusing at times. The first time I did the problem, I did it wrong. I calculated the number of pizza combinations Paula could have gotten incorrectly, I forgot to eliminate the doubles and I came out with a number of combinations that was much bigger that the actual number. But, I was patient and persistent with my work and was able to re-do the problem so that I could find the correct answer. After I re-did the problem, I was more careful and finished the problem easily. This habit will helped me grow because it helped remind me to be cautious and double check my answers. I will be able to use this habit in the real world because it is a skill that could prevent me from making similar mistakes again.