Overview
In this project we studied the Renaissance and Probability. Our class started with Game of Pig, a dice game, and Gambler’s Fallacy, a statement that every individual coin flip chance is unaffected by the rest. We then moved into the Renaissance project, picking a game that had originated before or during the time. This game had to involve or be based off of chance, our class continued into writing probabilities in PR[B or A] form and understanding 2-way tables. These were accomplished through the worksheets involving probability. One that I believe encompasses a majority of the concepts is ‘Who’s Cheating?’ This was a 2 part worksheet, first with Observed Results and Theoretical results. It revolved around a process to determine who was using substances versus who wasn’t. The process, which involved dice and coins, is a bit difficult to explain, so the original worksheet instructions will be linked above, along with my own worksheets. The process to determine who was cheating was a two-tiered process that can be illustrated using a tree diagram or a two-way table. For the ‘Observed Results’ portion, our class completed the process 36 different times and recorded our results. These were then put into different diagrams and tables and then we had to calculate the probability of each outcome. The second worksheet focused on the theoretical results and how we got them. This was also when we began to use the bracket-style for showing probability.
Probability: The chances of how likely something will turn (in games, choices, events, etc.)
Observed Probability: A probability of an event that is calculated through data that has been observed.
Theoretical Probability: A probability of an event that is calculated through how we expect an event to happen.
Conditional Probability: A probability of an event [A] that is calculated given that another event [B] has already happened.
Probability of Multiple Events: The chances of different events occurring calculated through additional individual or conditional probabilities multiplied by the probability of the first event.
Expected Value: A predicted outcome of an event(s) that is calculated by all possible possibilities of an event happened multiplied by the number of times the event happens.
Two-Way Table: A table that separates data into two distinguishable variables and totals, which are labeled joint and marginal probability outcomes respectively, it's very helpful for finding joint and conditional probabilities.
Tree Diagram: A diagram that branches out into different probabilities of an event, it's also helpful for joint and conditional probabilities.
Joint Probability: The probability of two events happening at the same time or together, the formula being Pr[A and B]= P[A | B] * P[B]
Marginal Probability: The probability of an event happening, regardless of a condition, usually seen as Pr[A] or Pr[B]
In this project we studied the Renaissance and Probability. Our class started with Game of Pig, a dice game, and Gambler’s Fallacy, a statement that every individual coin flip chance is unaffected by the rest. We then moved into the Renaissance project, picking a game that had originated before or during the time. This game had to involve or be based off of chance, our class continued into writing probabilities in PR[B or A] form and understanding 2-way tables. These were accomplished through the worksheets involving probability. One that I believe encompasses a majority of the concepts is ‘Who’s Cheating?’ This was a 2 part worksheet, first with Observed Results and Theoretical results. It revolved around a process to determine who was using substances versus who wasn’t. The process, which involved dice and coins, is a bit difficult to explain, so the original worksheet instructions will be linked above, along with my own worksheets. The process to determine who was cheating was a two-tiered process that can be illustrated using a tree diagram or a two-way table. For the ‘Observed Results’ portion, our class completed the process 36 different times and recorded our results. These were then put into different diagrams and tables and then we had to calculate the probability of each outcome. The second worksheet focused on the theoretical results and how we got them. This was also when we began to use the bracket-style for showing probability.
Probability: The chances of how likely something will turn (in games, choices, events, etc.)
Observed Probability: A probability of an event that is calculated through data that has been observed.
Theoretical Probability: A probability of an event that is calculated through how we expect an event to happen.
Conditional Probability: A probability of an event [A] that is calculated given that another event [B] has already happened.
Probability of Multiple Events: The chances of different events occurring calculated through additional individual or conditional probabilities multiplied by the probability of the first event.
Expected Value: A predicted outcome of an event(s) that is calculated by all possible possibilities of an event happened multiplied by the number of times the event happens.
Two-Way Table: A table that separates data into two distinguishable variables and totals, which are labeled joint and marginal probability outcomes respectively, it's very helpful for finding joint and conditional probabilities.
Tree Diagram: A diagram that branches out into different probabilities of an event, it's also helpful for joint and conditional probabilities.
Joint Probability: The probability of two events happening at the same time or together, the formula being Pr[A and B]= P[A | B] * P[B]
Marginal Probability: The probability of an event happening, regardless of a condition, usually seen as Pr[A] or Pr[B]
Renaissace- Inspired Game
The game my partner and I chose was Hazard, a dice game based off chance. The game hazard was created in England, mentioned Geoffrey Chaucer's Centerbury Tales in the 14th century. This game was often played for money with ordinary people, and there is a modern version of this game called craps. We chose this game to exhibit because it was a more different from my classmates and it wasn't as difficult. This game is played by first choosing a number 5-9, for example 6, which you choose before rolling the dice. If you roll your main then, you win, but if you roll a 2,3, or 11 then you lose (losing numbers depend on your main.) If you get anything other than your losing or main, then that becomes your chance. After having your chance, you roll again, and if you get your chance you win but if you get your main which is 6, you lose.
The game my partner and I chose was Hazard, a dice game based off chance. The game hazard was created in England, mentioned Geoffrey Chaucer's Centerbury Tales in the 14th century. This game was often played for money with ordinary people, and there is a modern version of this game called craps. We chose this game to exhibit because it was a more different from my classmates and it wasn't as difficult. This game is played by first choosing a number 5-9, for example 6, which you choose before rolling the dice. If you roll your main then, you win, but if you roll a 2,3, or 11 then you lose (losing numbers depend on your main.) If you get anything other than your losing or main, then that becomes your chance. After having your chance, you roll again, and if you get your chance you win but if you get your main which is 6, you lose.
Probability Analysis
What is the probability of rolling your main?
The probability of winning the game of Hazard is 4/36, and the probability of losing is 6/36.
(The picture below explains why this happens).
What is the probability of rolling your main?
The probability of winning the game of Hazard is 4/36, and the probability of losing is 6/36.
(The picture below explains why this happens).
I used the seek and prove why habit of a mathematician, because we found the answer to the probability of winning our game, and we used area diagrams to prove why the probability of wining is 5/36 and to see how we could come up with a different answer and testing our game various times. I think what made this project easier was the habit of staying organized. In my perspective I believe that, staying organized, is verye important in all projects. I think that being able to keep track of deadlines, worksheets, and work overall is something you must do to be successful. Being able to contjure and test came also from seek and prove why. Testing the main numbers and trying to see how we could create a better question and diagram. This habits definitely prove our success. They are the main drivers of our thinking and resolving problems.
The overall project was definitely something different and a new experience, my partner and I had struggles but we were able to get through this challenge. . A success for this project would defiantly be the probability factor and learning how to do the probability analysis. A challenge was defiantly gathering the games and learning how to execute them because It was really difficult to recognize some of the games. In the end, I think that everyones game turned out really well, and we overall did an awesome job and it was a great exhibition. I feel like I put lots of effort into this project because I was doing something with my game or my guild. Sometimes I did get confused and didn't ask questions but I hope to improve in that area and not be afraid of asking them.