Does it ever make sense to play the Lottery?
In a first semester probability course, students encounter combinatorics and point estimates such as the mean and median of a data set. A common example is the low odds of winning the lottery. When discussing the topic of point estimates, students are exposed to the idea of a “fair bet” or “fair game” - one in which the expected value of the random variable associated with the game is equal to the cost of participation or zero, depending on if a fixed cost is included in the game or tracked separately. This year, the Mega Millions had a jackpot in excess of one billion dollars. This had me thinking - mathematically, this is likely a fair game. But I still would expect to loose out playing it. In this article, I want to explore this idea further using the Mega Millions lottery as a particular example. ...