initial process |
When we first started we played our own Super Lotto of our own. The pay-in was the 2 extra credit points Mr. Carter had given us for free. There were 6 boxes, 5 for any number between 1 and 47, and there was a final box that had the mega number, which was a number between 1 and 27. We were also asked what we thought were the chances of actually winning the lottery. I had guessed one in a million.
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Formulas and equations learned |
We started with The Game of Pig, a game which introduced us to chance a choice. We had the choice to continue to roll our dice and not end our turn. But the chance of ending your turn automatically by rolling a 1. The sticky gum problem introduced us to probability. We had to prove why Ms. Elliott would only need 3 cents to get her 2 children two of the same color gumballs from a gumball machine that only has two colors and costs 1 cent. By being able to prove this we were also able to prove the lowest costs for any amount of gumballs and any amount of children. Roulette introduced the risk and reward type of game model backed up by actual probabilities to help us decide what we wanted to bet. Each of these probabilities affected the payout if you win which brought us into expected value. How much are casinos winning every time you play roulette? We solved this using the equation; E(X)=∑xipiE. It looks like a very complicated and difficult equation but it's actually very simple. You have to plug in the amount you can win for x and the probability of winning for 1 plus the amount you can lose for p and the probability or losing for the second i. With this you are able to find the expected value of winning. Which in this case, the casino won 5 cents for every dollar you played.
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We also used the Titanic statistics to answer the question if the women and children first order actually happened. We found of the probability of each persons survival rate. Then we looked a step closer and separated each category - men,women, and children- and found out their probability for surviving. We took this information and used conditional probability to figure out that the women and children first rule was indeed followed aboard the Titanic. This brings us back to the CA Super Lotto problem. We first had to learn all these skills in order to be able to understand what was happening with the questions we were given.
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Problem evaluation |
self evaluation |
This problem was a very fun problem to do. I felt like i learned a lot and all the probability stuff really made me have to practice and practice to really understand a concept. I did struggle a lot through this problem and that's what made this problem so great for me. Last semester I really wanted more things to make me struggle and the California super lotto gave me exactly that.
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This problem really made me think a lot about my math skills. I will admit, at times i really had given up on my skill in math because i was getting so many of the problems wrong. This really pushed me to practice and really want to understand the subjects. I always reminded myself that its okay to make mistakes, and this really encouraged me to share out my answers no matter if they were wrong or not.
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