## California Super Lotto

Here I am talking about tackling the California Super Lotto problem. In this problem we simulate the situation of buying a lottery ticket in the California Super Lotto. Of course the rules are: Pick any 5 numbers 1-47, Then pick a mega number 1-27. If your numbers match the winning numbers, you win!

What I am trying to do is answer these 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.

I think we decided to tackle this problem because we have been working and calculating the probability of situations, and what is harder and more interesting than trying to find the probability of winning the lottery! WE launched it the first day of our second semester and we launched by having our own little lottery game and if our numbers matched then we would get a lot of extra credit. We had a choice if we wanted to participate. If we didn't want to try to win the lottery then we got 1 point extra credit anyways, but if we joined and lost then you get no extra credit. I felt confident and decided to play and sadly, I ended up losing getting no numbers correct. I felt bummed after but it was fun and good start to getting me interested in this problem.

What I am trying to do is answer these 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.

I think we decided to tackle this problem because we have been working and calculating the probability of situations, and what is harder and more interesting than trying to find the probability of winning the lottery! WE launched it the first day of our second semester and we launched by having our own little lottery game and if our numbers matched then we would get a lot of extra credit. We had a choice if we wanted to participate. If we didn't want to try to win the lottery then we got 1 point extra credit anyways, but if we joined and lost then you get no extra credit. I felt confident and decided to play and sadly, I ended up losing getting no numbers correct. I felt bummed after but it was fun and good start to getting me interested in this problem.

When looking at this problem, (even though I feel confident when doing probability) I froze up and didn't know where to start. I talked and communicated with all my table mates to see if they had any starting ideas. We all were lost and I knew we needed a little boost to start get rolling so we called Mr. Anatole over to help. He recommended that we started out with a factor tree. He said take each of the numbers in the lottery and see what the probability of each number after you've chosen the number before and so on. When he explained that I was still a little confused then it reminded of how when we did other problems for example if we take out a red diamond card out of a deck of cards, you have to take one of of the category of red cards, diamond cards, and overall cards in the deck.

It led me to this solution. To multiply possibility after possibility, subtracting 1 each time because you take one possibility away. I got this answer and I felt really confident then I had it critiqued by a peer. I turns the mega number is missing from this equation!

I now put the mega number possibility in the mix and it me all the probability of winning. We know that this solution is correct because we took the max probability amount with every number and multiplied them together to give us the probability amount of the CA Super Lotto. My guess was actually really close to this, my guess was 38 million because that's California's population.

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.

## Problem Evaluation

I actually liked this problem because it really did push my thinking. I felt like all the other problems to prepare for this were very easy and I completed those with confidence the whole time. This problem actually pushed my thinking and froze me up sometimes which I admire.I think grew the most in checking my work and referring to my past references. It made me go back to worksheets and confirm I did the process correct which means it pushed me into having to check my work because I wasn't very confident in it.

## Self Evaluation

I have been very confident and consistent when it came to solving these probability problems over the past 6 weeks. The one thing I had trouble with sometimes was just starting the problem, knowing the first step. When learning a new math subject you are going to have trouble knowing what to do first. I wasn't the only one, many people had trouble knowing the first step but I'm sure after help with that first step they were rolling and completing questions with ease, because that's how I felt. I think I deserve an A because of how I not only got my work done really well but I felt like a leader at my table the way I help my table mates try to understand this subject at times.

## Peer Critique

Here is my peer critique!