Problem Statement:
To play the California super lotto you need to choose 5 different numbers between 1-47 these numbers can not repeat. You will also need to pick a number between 1-27, this number will be your mega number this number may repeat . In other to win you will have to match all 5 numbers you choose and also match the mega number. We had to find the probability of wining the California super lotto by trying to solve three different questions. 1.) How many different number combination are possible for a California super lotto ticket. ? 2.) What is the probability of winning the California super lotto ? 3.) If you match all six numbers, you win $8,000,000 . It costs $ 1 to play. What are you expected winnings ? Process and Solution: the process was picking five different numbers and a mega number after picking does five numbers and the mega numbers there was a list of couple of simple questions. We answers does and after we solved the 3 questions on top. What i first did was multiplyed 5 times 47 because you pick 5 numbers and since you have to pick a number between 1 and 47 that means 47 is the highest number you can pick. once multiplying that i got 235, that means we have 235 number combinations . i also multiply 1 times 27 because we had to pick only one mega number the 27 was because we can only pick a number between 1 and 27 . which that means there is 27 number combinations for the mega number. After finding the combinations i added both total combinations and i got 262 number combinations in total for both 5 numbers and mega number. To find the probability of wining the super lotto we had to multiply the following numbers: 5/47 . 4/46 . 3/45 . 3/44 . 1/43 and 1/27 as our mega number. the final answer 120/4,96962,360 which is the same as o.000000024 % After finding out your probability and picking your five numbers you pay 1 dollar and you have to match all six numbers in order to win the 8,000,000 price Problem Evaluation: I kinda liked the problem but also dislike because at the beginning of the semester i wasn't able to understand some parts (most parts) of the things we were learning but as the topic went by i started to understand and know i kinda get it a little more. Self Evaluation: I feel like i deserve an A because i really put all my effort in the work that i was doing i sometimes rush to get it done when i saw people were done, i would never leave anything blank if i dint know something i would write down a question or even ask people around me to help or explain n to me what i was stuck on. |
In the image above we found all the different number conbinatios possible for the California Super Lotto we choose 5 number 1-47 to find the conbinatios we multily5 and 47 because 5 numbers in total and the max number is 47 so that equals to 235. we also had to multiply 1 and 27 because we needed a mega number we choose 1 number and it had to be between 1 and 27 so its 1 times 27 that equals to 27. after finding out this numbers we had to add both 5 numbers and the mega number and we got 262 total number conbinations.
here we had to figure out the probability of wining the lotto so we multiply 5/47 . 4/46 . 3/45 . 3/44 . 1/43 and 1/27 as our mega number. the final answer 120/4,96962,360 witch is the same as o.000000024 %
here we had to calculate the wining that we were expecting we got a total of -0.806 we got this by doing E(X)= 8,000,000 (120/4,9696962360) + (-1) (4,96962,240/4,96962360) and that gave us -4009,962,240 divided by 4,969,962,360 and that equals -0.806
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