Something I am most proud of in the probability unit is my work in the gumball problem. During the gumball problem I was able to make a very well organized table to put my thoughts on paper. This organized table also helped me solve the equation to the problem given. Here is part of the table I made.
I hope to make more tables like this one in the future, because it easy to follow and show other people. When looking at this I could automatically see how each variable affected P(the variable that I made the dependent variable).
Two habits of a Mathematician I used in this unit are stay organized and look for patterns. I stayed organized in this problem by restraining my urge to just start randomly writing down my thoughts and actually thinking through the problem first(On the right, you can see my work from a previous unit. Look above to see improvement) After thinking through the problem, I proceed to make a table displaying changes due to variables in the problem. This makes it so I can recall the information I solved early in the problem, later on. This also helped with the second habit of a mathematician which was looking for patterns. In the tables I made to stay organized, I am easily able to identify different patterns and differences between each case.
The main mathematical ideas we went over in the probability unit are all important to the idea of probability. Simulations are when you go and create tests in order to find the experimental probability of an action. Some examples of this are the "Waiting for the Double", and the "Expecting the Unexpected" experiment. When we were trying to see the probability of events in the "Waiting for the Double", we used experiments in order to come up with a strategy. You can see an example of my work below, I like to write out my thinking.
Theoretical probability is when you use math to figure out probability of an event. For example, when we were doing the "Rug problems", we had to use equations in order to find the "expected value" of a certain color on a rug based off the probability of a dart landing on that color and the certain point values. The expected value has a lot of real life uses. For example, when you are gambling on something, you want to chose an option with slightly high probability with a large payoff. You can use expected value in order to find which one would earn you the most "in the long run".