In this paper, we consider some combinatorial and statistical aspects of the popular Powerball lottery game. It is not difficult for students in an introductory statistics course to compute the probabilities of winning various prizes, including the jackpot in the Powerball game. Assuming a unique jackpot winner, it is not difficult to find the expected value and the variance of the probability distribution for the dollar prize amount. In certain circumstances, the expected value is positive, which might suggest that it would be desirable to buy Powerball tickets. However, due to the extremely high coefficient of variation in this problem, we use the law of large numbers to show that we would need to buy an untenable number of tickets to be reasonably confident of making a profit. We also consider the impact of sharing the jackpot with other winners.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education