Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Calculate the Expected Value?
Calculate the expected value for playing mega millions with $1000 and winning a prize. Each ticket costing $1
PRIZE LEVEL- CHANCES OF WINNING PER- GAMEPRIZE
First- 1 in: 175,711,536- $88,000,000
Second- 1 in: 3,904,701- $250,000*
Third- 1 in: 689,065- $10,000*
Fourth- 1 in: 15,313- $150*
Fifth- 1 in: 13,781- $150*
Sixth - 1 in: 844- $10
Seventh- 1 in: 306- $7
Eighth- 1 in: 141- $3
Ninth- 1 in: 75- $2
- No BodyLv 410 years agoFavorite Answer
First find the expected value of one ticket, then multiply that value by 1000. Note that we should expect a negative value because the people/entities who fund these games like money:
EV = (1/175711536)(88000000) + (1/3904701)(250000) + (1/689065)(10000) + (1/15313)(150) + (1/13781)(150) + (1/844)(10) + (1/306)(7) + (1/141)(3) + (1/75)(2) + N
N is messy, so I'm leaving it separate. Its value is:
(1 - 1/75 - 1/141 - 1/306 - 1/844 ... etc)(-1)
So N will be slightly greater than -1, while all of the terms before N should sum to a positive number whose magnitude is slightly less than N's. Add everything together, then multiply the result by 1000 to get the expected value.
Note: The expected value is actually lower in reality since for larger winnings you have to pay tax, but we're ignoring that for this problem.
- ?Lv 45 years ago
expected value is the average possible value of x or the mean of a probablity distribution. if the probablity of x1 is p1 and x2 is p2 etc the formula is x1*p1+x2*p2+...xn*pn (the 1s, 2s and ns should be a subscript). to find the varience, find the expected value then use the formula (x1-expected value)^2*p1+(x2-expected value)^2*p2+...(xn-expected value)^2*pn the standard deviation is the square root of the varience. i hope the way i typed the formulas isnt too confusing.