Problem Statement
Ever since the beginning of this semester, we've been doing various problems that include probability so that we can get an easy grasp at the concept. When we first started this unit, we played the CA Super Lotto. The rules were pretty simple
- Choose any 5 numbers between 1-47 (these numbers will not repeat)
- Pick a mega number between 1-27 (this number may repeat)
- Match all 5 numbers and the mega number and you win!
- How many different number combinations are possible for a CA Super Lotto ticket?
- What is the probability of winning the CA Super Lotto?
- If you match all 6 numbers, you win $8,000,000. It costs $1 to play. What are your expected winnings?
Process and SOlution
At first, this problem had me stumped because I had no clue how to answer the questions since I didn't know how to find the different combinations, find the probability of winning, etc.
How many different number combinations are possible for a CA Super Lotto ticket?
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In order to find all possible combinations, my group and I used Permutations. Since we could only choose 5 numbers between 1-47, we started from 47 and kept subtracting one from the number until we had all 5 spots filled. For the mega number, we just took 27. When we had all the numbers in their slot, we multiplied everything together and got 4,969,962,460 possible combinations. Our solution is correct because when Anatole showed the class how he solved the problem, we got the same answer as him. Also, multiple groups got the same answer as I did.
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What is the probability of winning the CA Super Lotto?
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This answer is wrong because we forgot to multiply 27 which was the mega number.
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In order to calculate the probability of winning the CA Super Lotto, you would do the same method you did for finding all possible combinations. You would multiply 5,4,3,2,1 and get 120 which is now the numerator. Then you would take the number for all combinations which was 4,969,962,360 and that would be your denominator. So, the probability of winning is 120/4,969,962,360.
If you match all 6 numbers, you win $8,000,000. It costs $1 to play. What are your expected winnings?
In order to find the expected value, you would subtract 1 from the probability of winning which would be 41,416,352/41,416,353.
Then you would subtract 8,000,000 from 41,416,352. The answer would be -33,416,352/41,416,353 which is equal to -81 cents. This means that someone is losing 81 cents for every ticket they buy and that the CA Super Lotto is gaining 81 cents.
Then you would subtract 8,000,000 from 41,416,352. The answer would be -33,416,352/41,416,353 which is equal to -81 cents. This means that someone is losing 81 cents for every ticket they buy and that the CA Super Lotto is gaining 81 cents.
Problem Evaluation
I did not like this problem one bit. Probability was usually really easy for me, but for some reason this problem had me stuck and I couldn't quite figure out what to do without asking for help. Finding the expected value pushed my thinking because it took me a while to understand. The most challenging part of this problem was figuring out where to start. Since I was stuck on this problem, I had no idea where to start and that was challenging since I had a limited amount of time to finish it.
Self Evaluation
If I were to grade myself on this unit, I would give myself a B because even though I did do all of my work, I would get off task a lot. There were numerous occasions were I would get off topic and talk about random things and then get to my work. Also, if I was stuck on a problem or didn't understand what I was supposed to be solving, I wouldn't ask for help. Instead, I would talk to my table mates.
Edits
Bethany suggested that I include the what was the most challenging part of the problem, so that's what I did.
