Thursday, March 29, 2007

Death and Taxes: a Probabilistic Conundrum

Recently, I mentioned to my father that "taxes are more certain than death" this month. It is, after all, March 29th, and I'm planning to do my taxes today. I could die between now and April 15th, but I'm not counting on it.

The same calculus can be extended year after year. Even when I'm 70 years old, the probability of paying taxes will be well above the probability of dying in the current tax year. So how is it that it the long run, death is more certain than taxes (Keynes, 1923)? That is to say, the probability that one will die (which, as James Taranto loves to point out, is 1), whereas the probability that one will pay taxes is, while close to 1, not quite 1. Why do these compound differently over a lifespan?

Each event need only happen once. Let's consider only working adults; otherwise we have an easy way out. Thus, for a working adult, there is each year a very high probability of paying taxes and a low probability of death. In each year that he does not die, he faces similar probabilities the following year. Aye, there's the rub: we repeat this game - by construction - until he dies, though he may not have paid taxes in that time.

A wholly correct but somewhat unsatisfying answer to an altogether inane question.

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