Section 1
So far in math class we have been going deep into the topic of probability. So as of now, I think I am pretty good at probability, and know how to do most probability problems thrown at me. For the first semester, we were expected to learn these things; the definition of probability, what observed, theoretical, and conditional probability was, along with Probability of Multiple Events. Expected Value, Two-Way Tables, Tree Diagram, Joint Probability and Marginal Probability.
Section 2
Recently we had a schoolwide exhibition where we present the work we have done in each class to our audience such as friends and family. In Math class, the assignment for exhibition we were given was to make our own game that normal people played back in Renaissance times. I was partnered with Dylan Lewis, and Matthew Mau by choice. We chose to make a game called Wari.it was basically an even older version of mancala. Wari originated in Africa, and some parts of East Asia. The official name of the time, "Oware", means he/she marries. The legend said that a man and a woman had played the game endlessly, and to keep the game going, they got married. The game was also often played as a way of meeting others. It was a very social and inviting game that people would join just when walking by. The modern version of this game is mancala, although mancala was around invented near the same time as Wari, it was just played in other areas. My group and I chose to play this game because we all really enjoyed the game of mancala, and it was interesting to learn how other cultures had played the game. The only difference from Wari or formally known as “Oware” and Mancala is the backstory, and there is a factor of chance. For example some factors of chance in our game would be, if a roll is above an seven, player who rolled does not go. And if a double is rolled, player who rolled the double is out. We were also assigned to make instructions on how to play the game. So if people will know how to and also so we wouldn’t forget. Here are the rules:
So far in math class we have been going deep into the topic of probability. So as of now, I think I am pretty good at probability, and know how to do most probability problems thrown at me. For the first semester, we were expected to learn these things; the definition of probability, what observed, theoretical, and conditional probability was, along with Probability of Multiple Events. Expected Value, Two-Way Tables, Tree Diagram, Joint Probability and Marginal Probability.
- Probability
- the extent to which something is probable
- Observed Probability
- The value that is actually observed
- Theoretical Probability
- based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes
- Conditional Probability
- the probability of an event,, given that another has already occurred.
- Probability of Multiple Events
- As it sounds, the probability of two or more events happening
- Expected Value
- a predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.
- Two-Way Tables
- A table that has an x and y axis, displaying information on a certain topic
- Tree Diagram
- There are two "branches" (Heads and Tails) The probability of each branch is written on the branch. The outcome is written at the end of the branch.
- Joint Probability
- a statistical measure where the likelihood of two events occurring together and at the same point in time are calculated. Joint probability is the probability of event Y happening at the same time as event X
- Marginal Probability
- the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.
Section 2
Recently we had a schoolwide exhibition where we present the work we have done in each class to our audience such as friends and family. In Math class, the assignment for exhibition we were given was to make our own game that normal people played back in Renaissance times. I was partnered with Dylan Lewis, and Matthew Mau by choice. We chose to make a game called Wari.it was basically an even older version of mancala. Wari originated in Africa, and some parts of East Asia. The official name of the time, "Oware", means he/she marries. The legend said that a man and a woman had played the game endlessly, and to keep the game going, they got married. The game was also often played as a way of meeting others. It was a very social and inviting game that people would join just when walking by. The modern version of this game is mancala, although mancala was around invented near the same time as Wari, it was just played in other areas. My group and I chose to play this game because we all really enjoyed the game of mancala, and it was interesting to learn how other cultures had played the game. The only difference from Wari or formally known as “Oware” and Mancala is the backstory, and there is a factor of chance. For example some factors of chance in our game would be, if a roll is above an seven, player who rolled does not go. And if a double is rolled, player who rolled the double is out. We were also assigned to make instructions on how to play the game. So if people will know how to and also so we wouldn’t forget. Here are the rules:
- The Mancala board is made up of two rows of six holes.
- Four marbles are placed in each of the 12 holes.
- Each player has a hole/store (called a Mancala) to the right side of the Mancala board.
- The game begins with one player picking up all of the pieces in any one of the holes on his/her side.
- Moving counterclockwise, the player deposits one of the stones in each hole until the stones run out.
- If you run into your own store, deposit one piece in it. If you run into your opponent's store, skip it.
- If the last piece you drop is in your own store, you get a free turn.
- If the last piece you drop is in an empty hole on your side, you capture that piece and any pieces in the hole directly opposite.
- Always place all captured pieces in your store.
- The game ends when all six spaces on one side of the Mancala board are empty.
- The player who still has pieces on his side of the board when the game ends capture all of those pieces.
- Count all the pieces in each store. The winner is the player with the most pieces.
Section 3
Since we did spend all semester on probability, as you can guess, we had to figure out the factors of chance in our game actually happening. My group and I had to try and figure out the probability that if a roll is above an seven, player who rolled does not go. And if a double is rolled, player who rolled the double is out. We also decided why not find the probability of having the chance to go. So that is what we did in the picture below. Our final results is that each player has a 15/36 chance of rolling above a seven meaning that they are not able to go according to the rules of the game. He or she has a 21/36 chance of rolling under seven, enabling them to have a chance to go. And lastly they have a 6/36 chance of rolling a double which means they will be automatically disqualified. To get these probabilities we made an area diagram and shaded and marked the boxes accordingly. This way it was easy and convenient along with it being an efficient way to keep track of our data and probabilities we have collected. A mathematician strategy or habit my group and I used was to draw the problem out and make a table. Since we are all visual learners, drawing out the problem and looking at it physically was extremely helpful and basically guaranteed 100% accuracy in solving the problem unless we mess counting. Another thing my group and I did that is a habit or strategy of a mathematician was to be organized and efficient. We made sure we were organized by making a key for the diagram symbolizing how many boxes were marked for each factor of chance within our game. We were also efficient since we only used on area diagram for all 3 different factors of chance in our game while also keeping it extremely organized. Below is a picture of the work and calculations we did and a probability tree, basically simulating the game and the variables of chance.
Since we did spend all semester on probability, as you can guess, we had to figure out the factors of chance in our game actually happening. My group and I had to try and figure out the probability that if a roll is above an seven, player who rolled does not go. And if a double is rolled, player who rolled the double is out. We also decided why not find the probability of having the chance to go. So that is what we did in the picture below. Our final results is that each player has a 15/36 chance of rolling above a seven meaning that they are not able to go according to the rules of the game. He or she has a 21/36 chance of rolling under seven, enabling them to have a chance to go. And lastly they have a 6/36 chance of rolling a double which means they will be automatically disqualified. To get these probabilities we made an area diagram and shaded and marked the boxes accordingly. This way it was easy and convenient along with it being an efficient way to keep track of our data and probabilities we have collected. A mathematician strategy or habit my group and I used was to draw the problem out and make a table. Since we are all visual learners, drawing out the problem and looking at it physically was extremely helpful and basically guaranteed 100% accuracy in solving the problem unless we mess counting. Another thing my group and I did that is a habit or strategy of a mathematician was to be organized and efficient. We made sure we were organized by making a key for the diagram symbolizing how many boxes were marked for each factor of chance within our game. We were also efficient since we only used on area diagram for all 3 different factors of chance in our game while also keeping it extremely organized. Below is a picture of the work and calculations we did and a probability tree, basically simulating the game and the variables of chance.
Section 4
This project is as you know over. Throughout the project, my group and I along with myself personally has had a lot of challenges and successes. For instance, one of them being a game that we could do. We had to make sure the game was something we could easily get, and something we could easily replicate. We also made sure the game we chose was something we thought was fun and interesting, as well as for our audience. With these guidelines we went by, our field of renaissance games were extremely narrowed. We had trouble finding the game we wanted to play just by looking up renaissance games and using the links provided by our teacher, so my group and I collectively sat down and wrote down ideas on a paper that we thought was fun and something that was a possibility during the Renaissance. After about half an hour or so we stumbled upon Wari and chose to do it since it sounded a lot like mancala which we thought was fun and it's backstory is very interesting. We also knew it would be something we could easily have access to, all we needed was 2 di, and a mancala board which we got the day we decided to do the game we chose. Some other challenges in this project were trying to figure out how to calculate the factors of chance in our game, since this type of probability is a new type to us. Something that I think worked out well for us was us working together as a group since I feel like we collaborated and talked a lot about what we wanted for the project and what we wanted to do. We all agreed which made the work very easy and something that was almost fun. Another thing that I thought worked well was us sharing the workload and us giving each other feedback and how we would just bounce off of each other in a way which made this project actually quite easy, once we chose our game, it was really easy to kickoff and catch up and even past most of the other groups since our game was very easy to replicate and something we thought was fun so we didn’t mind doing the work and also working with each other since we have all been friends for a really long time, so we basically saw it as a time to hangout in class while also getting work done. Therefore making us efficient workers. We also made sure we finalized our product and made sure everything we needed was there in order to successfully perform the game and present it to our audience without messing up. Overall, this project was actually really helpful since we got to go deep into probability and learn much more than I think we would have at a regular school. I also feel like I learned that rolling two dice isn’t as simple as it seems, and I also learned that people didn’t just do art in the Renaissance, but they also played games.
This project is as you know over. Throughout the project, my group and I along with myself personally has had a lot of challenges and successes. For instance, one of them being a game that we could do. We had to make sure the game was something we could easily get, and something we could easily replicate. We also made sure the game we chose was something we thought was fun and interesting, as well as for our audience. With these guidelines we went by, our field of renaissance games were extremely narrowed. We had trouble finding the game we wanted to play just by looking up renaissance games and using the links provided by our teacher, so my group and I collectively sat down and wrote down ideas on a paper that we thought was fun and something that was a possibility during the Renaissance. After about half an hour or so we stumbled upon Wari and chose to do it since it sounded a lot like mancala which we thought was fun and it's backstory is very interesting. We also knew it would be something we could easily have access to, all we needed was 2 di, and a mancala board which we got the day we decided to do the game we chose. Some other challenges in this project were trying to figure out how to calculate the factors of chance in our game, since this type of probability is a new type to us. Something that I think worked out well for us was us working together as a group since I feel like we collaborated and talked a lot about what we wanted for the project and what we wanted to do. We all agreed which made the work very easy and something that was almost fun. Another thing that I thought worked well was us sharing the workload and us giving each other feedback and how we would just bounce off of each other in a way which made this project actually quite easy, once we chose our game, it was really easy to kickoff and catch up and even past most of the other groups since our game was very easy to replicate and something we thought was fun so we didn’t mind doing the work and also working with each other since we have all been friends for a really long time, so we basically saw it as a time to hangout in class while also getting work done. Therefore making us efficient workers. We also made sure we finalized our product and made sure everything we needed was there in order to successfully perform the game and present it to our audience without messing up. Overall, this project was actually really helpful since we got to go deep into probability and learn much more than I think we would have at a regular school. I also feel like I learned that rolling two dice isn’t as simple as it seems, and I also learned that people didn’t just do art in the Renaissance, but they also played games.