Overview
This project was all about probability and we learned about it in different ways. We had many different activities but the main product was a board game we were building. The definition of probability is the extent to which something is probable; the likelihood of something happening or being the case. Observed probability is a form of probability but it is done with real data or information. It is not in theory but in what actually took place. For example say I roll a die 3 times and a 1 or 2 means yes but a 3,4,5,6 means no. I get a 2, 4, and a 1. The observed probability of yes is 2/3 and no is 1/3. It is the probability of actual data. Theoretical probability is the opposite, and is the probability of something that hasn't happened in real life, only in theory. For example if I roll a die the theoretical probability of me getting a 3 is 1/6 since there are 6 different outcomes and 3 is one of those outcomes. It also takes into account that every side is equal, though. I like to think of conditional probability as two step probability. It is probability but it is affected by what happened earlier. For example if I have a bag of 3 red marbles, 2 blue marbles, and 1 green marble and I take a red one out there are 5 left. Now the probability of me pulling a blue marble is different than before I had taken a red marble. That is conditional probability.
Renaissance-Inspired Game
My renaissance game was called knucklebones. Knucklebones is played with 2 or more players and the only materials you need are 2 dice and maybe a piece of paper to keep track of score. Before you begin, you must set a score limit which you reach to win. I normally use fifty. One person starts by rolling the dice and keeping track of their number. Then it continues in order until it gets back to the first person. When he rolls again, he just keeps on adding on to score, since everyone's points are cumulative. It continues like that until one player reaches the set number. The first player to reach that number wins. There are different variations of the game but that one is most common. We made one change to the original game which was doubles. If you rolled doubles then you got to go again and keep going as long as you kept rolling doubles. It made it more interesting because if you got a 2, you had a chance to keep going and get a higher score. Knucklebones was actually the old term for dice, because they actually used to use the ankle bones of goats as dice. Each side looked different and had a different value. They do not actually know how the game originated but one theory is that the Greek figure Palamedes taught it to Greek countrymen during the Trojan War and it just spread from there. The game was played mainly by women and children but other forms of the game were played by men as well. It was played mainly in homes or at schools. I chose this game because it looked like a fun, simple game that could be played by people of all ages. It was not too hard or complicated so even a small child could understand it. I played it before I chose it and I got so into the game and I was having a lot of fun. I wanted other people to experience the fun I was having. The modern version of this game is jacks. It is still played all over the world by many different names such as taba or gonggi. Probability plays such a big role in my game because it is all about chance. It is about the way the dice rolls and lands. There is no skill in my game whatsoever. On a dice there are 6 sides so the probability of getting any number is 1/6. When you have two dice the probability changes. The best roll in this game is a 12 because it is a high score and you get to keep going. Since there is only one way to get a 12 the probability of getting it is 1/36. This is because there are 36 different outcomes and only one way to get 12.
Probability Analysis
For this activity, I am going to demonstrate a probability analyses that could happen in the game. It is basically a possible outcome and I am solving for the likelihood of that outcome. I am going to show the probability of getting to 50 perfectly or getting it in 5 roles without anyone else going. This is only possible by getting four twelves in a row. The fifth role could be anything since you only need two more to get to 50. First you must find the probability of getting 12, which is 1/36 since there are 36 possible outcomes and only one way to get 12. Then you do 1/36 to the fourth power since you need 4 roles with a 12. This gets you 1/1679616. The fifth role could be anything which means you multiply by 1/1 and you still get the same answer.
Reflection
This project was somewhat challenging but not extremely challenging. It was a good amount of challenging because we struggled and learned from it but not to the point where we didn't know what to do anymore. Growth comes through struggle, and I think I grew a lot during this project. The skills and content I learned will help me in the future from college to the real world. One thing that worked really well for me was having the worksheets passed out to everyone. Almost all the work we did was individually which I enjoyed because I could go at my own pace. I did not have to rush or wait for the rest of the class, and I felt like I could focus more. I think this style helps me succeed and I hope we can keep doing this in the future. One thing I regret is throwing away the dice I made for my game. I threw them away too soon because I did not think I needed them but I did not take any pictures. Now I don't have any pictures of my game or exhibition. Overall, this was a good project because I was pushing myself and I grew a lot. I made mistakes but that is what helps us become better mathematicians. I enjoyed it too and this work will transition into the real world.
This project was all about probability and we learned about it in different ways. We had many different activities but the main product was a board game we were building. The definition of probability is the extent to which something is probable; the likelihood of something happening or being the case. Observed probability is a form of probability but it is done with real data or information. It is not in theory but in what actually took place. For example say I roll a die 3 times and a 1 or 2 means yes but a 3,4,5,6 means no. I get a 2, 4, and a 1. The observed probability of yes is 2/3 and no is 1/3. It is the probability of actual data. Theoretical probability is the opposite, and is the probability of something that hasn't happened in real life, only in theory. For example if I roll a die the theoretical probability of me getting a 3 is 1/6 since there are 6 different outcomes and 3 is one of those outcomes. It also takes into account that every side is equal, though. I like to think of conditional probability as two step probability. It is probability but it is affected by what happened earlier. For example if I have a bag of 3 red marbles, 2 blue marbles, and 1 green marble and I take a red one out there are 5 left. Now the probability of me pulling a blue marble is different than before I had taken a red marble. That is conditional probability.
Renaissance-Inspired Game
My renaissance game was called knucklebones. Knucklebones is played with 2 or more players and the only materials you need are 2 dice and maybe a piece of paper to keep track of score. Before you begin, you must set a score limit which you reach to win. I normally use fifty. One person starts by rolling the dice and keeping track of their number. Then it continues in order until it gets back to the first person. When he rolls again, he just keeps on adding on to score, since everyone's points are cumulative. It continues like that until one player reaches the set number. The first player to reach that number wins. There are different variations of the game but that one is most common. We made one change to the original game which was doubles. If you rolled doubles then you got to go again and keep going as long as you kept rolling doubles. It made it more interesting because if you got a 2, you had a chance to keep going and get a higher score. Knucklebones was actually the old term for dice, because they actually used to use the ankle bones of goats as dice. Each side looked different and had a different value. They do not actually know how the game originated but one theory is that the Greek figure Palamedes taught it to Greek countrymen during the Trojan War and it just spread from there. The game was played mainly by women and children but other forms of the game were played by men as well. It was played mainly in homes or at schools. I chose this game because it looked like a fun, simple game that could be played by people of all ages. It was not too hard or complicated so even a small child could understand it. I played it before I chose it and I got so into the game and I was having a lot of fun. I wanted other people to experience the fun I was having. The modern version of this game is jacks. It is still played all over the world by many different names such as taba or gonggi. Probability plays such a big role in my game because it is all about chance. It is about the way the dice rolls and lands. There is no skill in my game whatsoever. On a dice there are 6 sides so the probability of getting any number is 1/6. When you have two dice the probability changes. The best roll in this game is a 12 because it is a high score and you get to keep going. Since there is only one way to get a 12 the probability of getting it is 1/36. This is because there are 36 different outcomes and only one way to get 12.
Probability Analysis
For this activity, I am going to demonstrate a probability analyses that could happen in the game. It is basically a possible outcome and I am solving for the likelihood of that outcome. I am going to show the probability of getting to 50 perfectly or getting it in 5 roles without anyone else going. This is only possible by getting four twelves in a row. The fifth role could be anything since you only need two more to get to 50. First you must find the probability of getting 12, which is 1/36 since there are 36 possible outcomes and only one way to get 12. Then you do 1/36 to the fourth power since you need 4 roles with a 12. This gets you 1/1679616. The fifth role could be anything which means you multiply by 1/1 and you still get the same answer.
Reflection
This project was somewhat challenging but not extremely challenging. It was a good amount of challenging because we struggled and learned from it but not to the point where we didn't know what to do anymore. Growth comes through struggle, and I think I grew a lot during this project. The skills and content I learned will help me in the future from college to the real world. One thing that worked really well for me was having the worksheets passed out to everyone. Almost all the work we did was individually which I enjoyed because I could go at my own pace. I did not have to rush or wait for the rest of the class, and I felt like I could focus more. I think this style helps me succeed and I hope we can keep doing this in the future. One thing I regret is throwing away the dice I made for my game. I threw them away too soon because I did not think I needed them but I did not take any pictures. Now I don't have any pictures of my game or exhibition. Overall, this was a good project because I was pushing myself and I grew a lot. I made mistakes but that is what helps us become better mathematicians. I enjoyed it too and this work will transition into the real world.