# Calculating an Expectation

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.