Problem Statement:
In this problem we had to answer 3 specific questions that we had to respond the first one was, How many different combinations are possible for a CA super lotto ticket? When answering this question we would be capable to answer the next question which was, What is the probability of winning the CA super lotto? When you answer each question it gets easier to answer the following ones the last questions was, If you match all 6 numbers, you win $8,000,000. And every time you play it costs $1. What are you expected winnings?
The interesting thing of this is that there's 3 rules which you have to follow in order to play the game. The rules are very simple, the first rule is that you have to choose 5 numbers between 1-47 and this number cannot repeat, the second rule is that you have to choose a mega number between 1-27 and those number can repeat, and the last rule was, to be able to win, all numbers had to be the same it would be the same case for the mega number and you win.
The interesting thing of this is that there's 3 rules which you have to follow in order to play the game. The rules are very simple, the first rule is that you have to choose 5 numbers between 1-47 and this number cannot repeat, the second rule is that you have to choose a mega number between 1-27 and those number can repeat, and the last rule was, to be able to win, all numbers had to be the same it would be the same case for the mega number and you win.
Process & Solution
Initial Attempts:
How many different number combinations are possible for a CA super lotto ticket?
To find the different combinations you need to multiply each probability (number) and that gives you how many combinations you can make with all the numbers together which is 4,969,962,360. When they gave me the paper with the question, I read the first one and I had no idea where to start, and I was very confused, someone explained to me that in order to know what was happening in the question i had to focus on the important words that would help me define , how to understand the question and when I did, I realized I had to find the combinations of each probability so I multiplied all of them including the mega number and that's how I got the answer. How I know this is right is because we discussed it in class.
To find the different combinations you need to multiply each probability (number) and that gives you how many combinations you can make with all the numbers together which is 4,969,962,360. When they gave me the paper with the question, I read the first one and I had no idea where to start, and I was very confused, someone explained to me that in order to know what was happening in the question i had to focus on the important words that would help me define , how to understand the question and when I did, I realized I had to find the combinations of each probability so I multiplied all of them including the mega number and that's how I got the answer. How I know this is right is because we discussed it in class.
What is the probability of winning the CA super lotto?
We started this problem by looking at the little boxes, every time we used a probability we had to cancel out each box, which meant that we had already used our probability and we had to decrease the number at the top. Ethan helped me to better understand how this works, because when we answered the question I didn't know why was the answer that, but then I got confused and Lidia told me that when you try to find the winning for the probability, each time you use a box your probability starts decreasing and when that happens you multiply each one of them without counting the overlaps and that gives you the answer above.
We started this problem by looking at the little boxes, every time we used a probability we had to cancel out each box, which meant that we had already used our probability and we had to decrease the number at the top. Ethan helped me to better understand how this works, because when we answered the question I didn't know why was the answer that, but then I got confused and Lidia told me that when you try to find the winning for the probability, each time you use a box your probability starts decreasing and when that happens you multiply each one of them without counting the overlaps and that gives you the answer above.
If you match all 6 numbers, you win $8,000,000. It costs $1 to play. What are you expected winnings?
In order to answer this question we had to know the probability, so when answering question 2 it would help us with this question because that give us the answer, this was the only thing that I knew at the time but then Lida told me that I had to use the expected value formula because that's what Mr. Carter told us it would be helpful to do so that's what I did and it got clearer for me to understand. We just plugged in the payouts and the probability that we got from the last 2 questions and that gave me the answer.
In order to answer this question we had to know the probability, so when answering question 2 it would help us with this question because that give us the answer, this was the only thing that I knew at the time but then Lida told me that I had to use the expected value formula because that's what Mr. Carter told us it would be helpful to do so that's what I did and it got clearer for me to understand. We just plugged in the payouts and the probability that we got from the last 2 questions and that gave me the answer.
Problem Evaluation
Did you like this problem? What pushed your thinking?What do you think you got most out of?
I enjoyed this problem a lot because from the first explanations that people were given I understood and it didn't take a lot of time for me to be able to explain it to someone else. My classmates were pushing me to get out of the bubble of thinking just in one way to solve the problems and having those techniques helped me to move on. I think I am more capable of thinking more, like getting more ideas from my classmates to then conclude with my own idea and answer.
I enjoyed this problem a lot because from the first explanations that people were given I understood and it didn't take a lot of time for me to be able to explain it to someone else. My classmates were pushing me to get out of the bubble of thinking just in one way to solve the problems and having those techniques helped me to move on. I think I am more capable of thinking more, like getting more ideas from my classmates to then conclude with my own idea and answer.
Self Evaluation
What grade should you receive?Why?
I think in a scale of 1-10 I will give myself an 8.5, because I have pushed myself to understand it but I didn't push myself enough to be capable to think out of my comfort zone. I asked question during the process of solving this problem with my classmates but I think I didn't ask specific questions that could have been more helpful in the future when solving this kind of problems, in a different context.
I think in a scale of 1-10 I will give myself an 8.5, because I have pushed myself to understand it but I didn't push myself enough to be capable to think out of my comfort zone. I asked question during the process of solving this problem with my classmates but I think I didn't ask specific questions that could have been more helpful in the future when solving this kind of problems, in a different context.