Problem Statement
What we had to do in this problem is to figure out what the probability of winning the California Super Lotto is. We had all the numbers, (1/47) and the mega numbers (1/27). All we had to do is find a way to calculate the chances of winning the Super Lotto. We also had to answer these 3 questions:
1. How many different number combinations are possible for a CA Super Lotto ticket?
2.What is the probability of winning the CA Super Lotto?
3. If you match all 6 numbers, you win $8,000,000. It cost $1 to play. What are your expected winnings.
1. How many different number combinations are possible for a CA Super Lotto ticket?
2.What is the probability of winning the CA Super Lotto?
3. If you match all 6 numbers, you win $8,000,000. It cost $1 to play. What are your expected winnings.
Process & Solution
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At first, I didn't really know what to do but then I got started after I googled the answer. Now Mr.Ginsberg, being the great mathmetician he is, decided to come by and peek me with the questions of, " How do you know that is right?"" What is the process of getting the answer?" etc. Soon, I figured out that the answer was going to involve dependent probability. I knew this because we had 47 numbers that we could choose from (total 5) and that they could not be used again. So if you see to the top right of the picture (right), you can see that I did 5/47, 4/46, 3/45, 2/44 and 1/43. Notice how the denominators are always constantly going down by 1. Again, this happens because the rules stated that once a number (out of 47) was chosen, it could not be used again. Example:
Normal #'s 1,2,3,4,5 Mega #'s 1 This is right! |
Anyways, having these denominators all done, I had to move to the numerators. Numerators was slightly easier because it was just doing 5! (5x4x3x2x1)(5 Factorial). I knew I had to do this because I had to find out all of the ways the winning numbers could be arranged.
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You wanna get the expected value of the ticket, so you have to take your expected winnings which is 8 million dollars and you put it with the probability of winning. You bought a $1 ticket of course so you you have to minus 1 from the probability of winning and put it in a fraction. The probability of losing over the probability of winning. Then you take the numerator which is the probability of losing and minus that from you winnings which equals to -.81 which means you lost 81 cents for buying that lottery ticket.
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Problem Evaluation
I kind of liked this project because at first, it was really out of hand for me because I didn't know what to do. After I got help from Mr.Ginsberg, I got rolling and just knew what to do after that.
Self Evaluation
I felt like I did a really good job on this problem because I pushed myself to find more and more information about the propabilities of winning the CA Super Lotto. I also have improved my leadership/teacher role by teaching people my methods and how I got my aswer. I deserve full credit on this problem because I felt like I was on top of everything and kept answering questions that were being asked.
