What is the California super lotto problem?
At the begging of this semester we played the "California super lotto" as a class but it was a little different. We were able to bet free extra credit points for a chance to win 20 dollars from Mr. Carter. There was about a total of about 2 kids who actually decided to put up those extra credit points .
Basics of the initial problem:
You had to choose 5 numbers between 1-47 and the numbers could not overlap. We also had to pick a mega number between 1-27, this number could overlap. In order to win you had to match all five numbers including the mega number, in any number.
After initial problem:
After we looked at that part of the problem we learned about probability and every topic we would need to understand the lotto problem.
Basics of the second part:
You had to find how many total number combinations were possible in the CA super lotto. Then you had to find the probability of winning the super lotto. Finally you had to find out your expected winnings if you match all 6 numbers, pay 1 dollar to play and win 8,000,000 dollars.
Basics of the initial problem:
You had to choose 5 numbers between 1-47 and the numbers could not overlap. We also had to pick a mega number between 1-27, this number could overlap. In order to win you had to match all five numbers including the mega number, in any number.
After initial problem:
After we looked at that part of the problem we learned about probability and every topic we would need to understand the lotto problem.
Basics of the second part:
You had to find how many total number combinations were possible in the CA super lotto. Then you had to find the probability of winning the super lotto. Finally you had to find out your expected winnings if you match all 6 numbers, pay 1 dollar to play and win 8,000,000 dollars.
Initial guess
My initial guess for the probability of winning the lottery, was 1 in 800,000. To be completely honest the only reason I came up with this number is because that first day when we played the "super lotto" no one won so I guessed that it would be a a very low probability. I chose 1 in 800,000 because so many people said 1 in 1,000,000 and I didn't want to be basic.
How I found out how many different number combinations there are.
The first thing I did was multiply 47x47x47x47x47x27 because you need to pick out 5 numbers (there's 5 forty sevens) between 1 and 47 and the 27 represents the mega number which you had to be between 1 and 27. Although I was on the right track I later realized that I was wrong. I figured out that the first forty seven would be going down by one each time (47x46x45x44x43x27) because since the numbers can't overlap once you pick out one number the sample space shrinks by one.
How I found out the probability of winning the super lotto
To find the probability of winning the lotto what I did was take the 5/47 that represents the 5 numbers you had to chose and the numbers you could chose from so since once you take one number out it shrinks because you can't pick out a number you already took out. So I multiplied all the possibilities and 1/27 to represent the mega number. After you find the answer to that you divide the top from the bottom to get the probability. Which ends up being a very low number.
How I found the expected value of a 1 dollar ticket
What I did to find the expected value is I used the expected value formula we learned in class. I'm not sure the exact formula but the way I did it for this problem was e(x)= payout (probability of winning) + (-1) (probability of loosing)
Problem evaluation
I personally really liked this problem. I feel like this problem challenged me enough, (especially remembering when the sample space changes) but was still really fun and I really liked how we learned each topic we needed to solve this project by playing a game.
Self evaluation
I am very proud of myself with this problem. I felt like it went by faster and easier, while still being challenging of course, than it would have in the first semester. I feel like I have personally really advanced in my growth mindset and I'm having a really fun time in math class all because I changed my attitude (which was very hard by the way) toward the subject. I would give myself an A because I feel like I really pushed myself to the best of my ability and did everything I could to understand what I was doing.