Playing the Odds: Putting Powerball in Perspective

JackpotToday’s fun math fact, in honor of the largest Powerball lottery jackpot ever:

If you have to drive more than a third of a mile to buy a Powerball lottery ticket, you’re more likely to die in a traffic accident than win the lottery.

My calculations: In 2013, the latest year figures are available, 32,719 Americans died in traffic accidents, according to the Federal Highway Administration. That same year, Americans drove a total of 2,972,287,000,000 vehicle miles (that’s just shy of 3 trillion), according to the Insurance Institute for Highway Safety. That yields 1 death per 90,842,843 miles driven, or a 0.000001100% chance of death per mile driven. Meanwhile, the odds of winning Powerball on a single ticket are 1 in 292,201,338, or 0.000000342%.

As a result, you’re 3.21 times more likely to die while driving a mile than you are to win Powerball on a single ticket. The odds equalize when driving 1/3.21 or 0.3109 miles. Thus, my conclusion above.

Corollary: If you’d like to have better odds of winning than dying, you need to buy at least three Powerball tickets per mile driven. Your chance of winning is still infinitesimal, but at least it’s better than your chance of a traffic fatality.

Educational Aside: Examples like this are why I think that statistics, not calculus, should be a required mathematics course at the high school or college level. Calculus is interesting and important, but it’s not as broadly applicable as stats. If more adults had a better understanding of things like expected value, we might make more rational decisions individually and as a society.

Image: “Jackpot Modern Casino,” Flickr, CC BY-NC-SA

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