University of Minnesota, Twin Cities School of Statistics Charlie Geyer Home Page John Corbett Home Page
Updated Feb 14, 2006.
To calculate any expectation you multiply the probability of each outcome by the amount you win for that outcome and sum. For the fixed prizes in the PowerBall lottery, the relevant numbers (taken from http://www.powerball.com/powerball/pb_prizes.asp) are
| event | prize | probability | product |
|---|---|---|---|
| match 5 | $200,000 | 1 / 3563608.83 | 0.05612 |
| match 4 + powerball | $10,000 | 1 / 584431.85 | 0.01711 |
| match 4 | $100 | 1 / 14254.44 | 0.00702 |
| match 3 + powerball | $100 | 1 / 11927.18 | 0.00838 |
| match 3 | $7 | 1 / 290.91 | 0.02406 |
| match 2 + powerball | $7 | 1 / 745.45 | 0.00939 |
| match 1 + powerball | $4 | 1 / 126.88 | 0.03153 |
| powerball | $3 | 1 / 68.96 | 0.04350 |
0.1971151
The last column contains the products of the numbers in the first two columns -- the amount of the prize times the probability of winning the prize. Adding the third column gives $0.19712. That's the expected value of the fixed prize winnings for one $1 ticket. It excludes any jackpot winnings, which vary with the size of the jackpot.
To see how the probabilities are calculated, see the about odds page of the Minnesota Lottery.