Lightning, Lotteries, and Probability

People often claim you have more chance of being struck by lightning than of winning the lottery. The argument appears to be that one Canadian in 5 million is struck by lightning every year, while your chances of winning the standard 6/49 lottery are about one in 14 million, and one in 5 million is a higher probability than one in 14 million. However, this reasoning is unsound.

The problem is that these two probabilities are not comparable. The estimate of the probability of being hit by lightning is an empirical one, derived from observation, and applies to an entire year's worth of thunderstorms. The estimate of the probability of winning the lottery is a mathematical one, derived from a formula which applies to a single drawing of the lottery.

We could derive from the first estimate the probability of being struck by lightning at the time the lottery number is drawn, which would provide a fairer comparison (and one which would favour the lottery), but the more important issue is why we would want to do that. The frequency of an event relative to electrocution by lightning is not a standard of worth. For example, the probability that an individual Canadian will become prime minister in the next year is lower then the probability that he or she will be struck by lightning, but no one would conclude that that difference in probabilities tells us anything about the value of the Canadian political system.

Lightning, Lotteries, and Probability © 2001, John FitzGerald