Problem Statement- California Super Lotto Problem At the beginning of this semester. Mr.Carter had the class play a different version of the California super lotto. If you wanted to play for a chance to win $20 from him, you had to give up the chance of two free extra credit points. The whole class had to choose 5 numbers 1-47 ( each number has to be different) and a mega number 1-27 ( this number can match any of the 5 numbers. Only two people in our class wanted to bet our two extra credit points to win $20. nobody in our class won. Now we are finding the probability of winning the California super lotto. looking at how many different combinations that is possible. what's the possibility of winning. If you match all 6 numbers, you win $8,000,000, it costs $1 to play, what are your expected winnings?
Process & solution- 1) how many different number combinations are possible? first you have to look at the sample space. and as you're choosing numbers 1-47, the amount of numbers that you can choose gets smaller each time. We lined up numbers 43-47 and the mega number. Then we multiplied those numbers together and the total combinations that we got was 4,969,962,360.
2) what is the possibility of winning the CA super lotto? we looked at how many combinations are possible. 4,969,962,360. and we have to make the sample space smaller each time because the amount of numbers left gets smaller, ( 5/47, 4/46, 3/45, 2/34, 1/33) the same with how many number you've chosen already. Then we have to have to show how many possible numbers are available for the mega number. (1/27). after we do that we have to multiply it all together. then we get 120/4,969,962,360 and if you divide those two together you get 0.000000024%
3) If you match all 6 numbers, you win 8,000,000. it costs $1 to play. What are your expected wins? for this problem we have to use expected value to find out the expected winnings. E(x) = payout ( / ) + (-1) ( / ) we the put E(X)= 8,000,000 (120 / 4,969,962,360)+ (-1) (4,962,962,240/ 4,969,962,360) we got the 4,969,962,240 from subtracting 120 and 4,969,962,360. and then we have to multiply the payout by 120. that gets us 960,000,000. then divide 960,000,000 by 4,969,962,360 and divide the last two numbers. and once we have the decimals that we got from dividing. we got 0.193160416611284 and 0.999999975854948 . we then have to subtract those two together and we get our final answer. -0.80.
Problem Evaluation- I really enjoyed doing this problem because I understood how to do probability and how to use expected value. Something that pushed my thinking was the last part of the problem because I didn't know how to write out the expected value formula and how to get the number in the third parenthesizes, the 4,969,962,240. But then I asked for help at my table and then I understood that I had to subtract the payout from the total combinations. I liked this unit because I understood what probability is and how people use it while gambling.
Self Evaluation- If I were to grade myself on this unit I would give myself an A+. I think I deserve this grade because during this unit I was able to think on my own without asking others for help. Also for helping people at my table and explaining what we were doing in class and how to do probability.
Edit Section- critiques I got from my peers include the first attempt or your thoughts on how you solved the problem I worked with two other people to solve this problem and at first we were all confused because we didn't know how to start the problem so we asked Mr. Carter for help and we were able to start the problem. maybe separate the text because seeing the numbers together is confusing (I made edits in the write up by making all the number bold)
Explain the Equation on question number 3 expected value is E(X). and you have to use it like E(X)= payout (/)+(-1) (/).
so for this problem the payout would be $8,000,000 because that's how much we would win.
the first two numbers in the first parenthesis would be 120 and 4,969,962,360. because that's what we got in question two.
then it would be +(-1) because you would pay a dollar to enter the lottery
the last two parenthesis would be 4,969,962,240 and 4,969,962,360. we got the first number from subtracting 120 by 4,969,962,360.
then we have to multiply the payout by 120, getting you 960,000,000.
that changes the equation to (960,000,000 / 4,969,962,360) - ( 4,969,962,240 / 4,969,962,360)
you divide each side which equals 0.193160416611284 and 0.999999975854948
then you subtract those from each other and that gets you the final answer, -0.80