Problem Statement
In this the Gumball Dilemma problem of the week, we had to use theoretical probability in order to figure out the price of how many of the same color gum balls were needed to feed a certain amount of identical siblings. Theoretical probability is the probability that a certain outcome will occur, as determined by reasoning or calculation. We had to solve several self made problems and try to find a pattern or an equation.
Process Description
The process I used was making a small chart like this one here. I sectioned off three sections. One for the amount of identical siblings, one for the amount of different colors of gum. Not looking for a pattern, I wrote down several kid/gum ball combos and didn't really see a pattern. Then, I took a look at each individual problem and found an equation. I knew that there was an equation somewhere in there, but didn't know how to write it out. After working around each combo, I eventually got the equation:
((k-g)-g)+1=C
((k-g)-g)+1=C
Solution
In the end of the problem, I found an equation that will determine the highest cost of the amount of same color gum balls that the identical siblings want. I am sure that this equation will work every time for this problem. I have tested it over ten times and it worked every time. Here is an example of the equation in action:
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Self-Assessment and Reflection
For the Gum Ball Dilemma POW, I would give myself a 10/10 because I both contributed greatly when we had group share outs, and presented my fair share of work for my group. I also think that I deserve this grade because I explored this problem very well and tried to find multiple ways to solve it, whether it'd be a pattern or equation. The Habit of Mathematician I think that I used most would have to be solve a simpler problem because what I did to solve for the equation was break down different parts of the original problem, and look for a pattern that allowed me to construct the equation.