PROBLEM STATEMENT:
The California super lotto its a lottery game where you can win a lot of money but you have an almost impossible probability of winning it.
it consists of you picking 5 numbers between 1 -47 and a mega number that is from 1-27 if you match the 6 numbers you win a certain high amount of money. for this problem we have 3 questions: 1) how many different combinations are possible for the CA super lotto? 2)what is the probability of winning the CA supper lotto? 3)If you match all 6 numbers, you win 8 million dollars. It costs $1 per ticket. What are your expected winnings? |
Process and Solution:
1) To solve how many possible combinations we multiplied all the sample spaces and we got 4,969,962,360 for this we jus multiplied 47 x 46 x 45 x 44 x 43 x 27.
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2)when we first saw we thought it was gonna be difficult to know but with Mr.Carter's help we saw that if we made the sample spaces fractions and how many chances of getting each fraction was we just multiplied 1 x 1 x 1...... and how obvious it was the answer was 1 so the chances of winning were 1/4,969,962,360
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3)This question was more easy because we learned how to do this before. What we did is that we wrote the chances of winning (1/41,416,353) and we multiplied it by the winning prize (8,000,000). Then me and my team multiplied the chances of loosing (41,416,352/41,416,353) by how much you loose which is how much you bet $1(-1). After we multiplied them, we subtracted what we got
(8,000,000/41,416,353 - 41,416,352/41,416,353) and got a total of -33,416,352/41,416,353 which equals -0.81. This is bad because it means that for every buck spent, the CA super lotto gets $0.81.
(8,000,000/41,416,353 - 41,416,352/41,416,353) and got a total of -33,416,352/41,416,353 which equals -0.81. This is bad because it means that for every buck spent, the CA super lotto gets $0.81.
Problem evaluation
At the end, I really enjoyed learning calculating probability through this problem. I really felt like my thinking process was being challenged because most of this was new material even when in my other school I learned basics of this such as the probability of winning and expected winnings over time. And the most important thing I learned is that lotteries and casinos in a long run make you loose money.
Self evaluation
In this unit, I have learned a lot of new material such as how to calculate probabilities. At first I wanted to try to figure it out myself but when Mr.Carter came to help I asked questions and in some point I understood it. I was even more happy when I understood it good in a point that i contributed more with my team, I even helped my group members. I think I deserve a B because my discipline in class but out of that im good.