Problem Statement:
What is the probability of winning the California Super Lotto? What are the possible combinations?
There are 5 numbers you can choose from 1-47 plus a mega number from 1-27. In order to win the lottery, you have to have your numbers match the randomized
What is the probability of winning the California Super Lotto? What are the possible combinations?
There are 5 numbers you can choose from 1-47 plus a mega number from 1-27. In order to win the lottery, you have to have your numbers match the randomized
Process & Solution:
For the “CA Super Lotto Problem” our goal was to find the probability of winning the lottery. My initial guess for the odds of winning the CA Super Lotto was 1 in 41 million. The first problem we began solving was “How many different number combinations are possible for a CA Super Lotto ticket?” My answer for this was 4,969,962,360. I got this answer by multiplying 47*46*45*44*43*27, I chose to multiply these numbers because they represent the amount of numbers available to chose from the possible numbers in the winning lotto ticket. After, I moved on to answering the next question which is “ What is the probability of winning the CA Super Lotto?” My answer for this was 1 in 41,416,353. I solved this problem by multiplying 5*4*3*2*1 which gave me 120. I chose to multiply those numbers because I was trying to figure out the amount of ways 5 numbers can be arranged. I got my answer and made it a fraction: 120/4,969,962,360. I then simplified my fraction and got 1/41416353. The last question I solved was “If you match all 6 numbers, you win $8,000,000. It costs $1 to play. What are your expected winnings?” My answer for this was that you lose 83 cents. I got this answer by plugging in numbers to: E(ticket)=8,000,000(P(win))+(-1)(P(loss)) From this equation I simplified it to: .16+(-.999) from this I got -.83 which tells me that I lose that amount of money. |
Problem Evaluation: I enjoyed working on this problem because it was the right amount of challenge for me. I got to ask questions and get help but I was also able to work things through by myself and get far into the problems. I think what most pushed my thinking was working with a different scale of numbers. In this problem, the numbers were either really small or really big and I think that made it more fun for me. During this math problem I was able to develop more efficiently my skill of using the knowledge I already have and use that to solve new challenges.
Self Evaluation: If I were to grade myself on this unit I would give myself an A. I completed all of my work efficiently and thoroughly enough so that I had a good understanding of the problem. Although I did sometimes get stuck on problems, I asked questions and was able to further understand the question. There were times, however, where I would slack off and talk to my peers instead of getting my work done first. Overall, I think I did a pretty good job in this unit and am very proud of what I have completed this far into this new semester.