Max R. P. Grossmann

Statement

For any incidence $x$ per year and 100,000 persons, calculate $x/13$ to obtain the approximate percent chance of having the event happen at least once in your life.

This rule of thumb works well for incidences up until approximately 390.

Example

At the time of writing, the intentional homicide rate in Saint Pierre and Miquelon was 16.5 per 100,000 people and year. This means that there is an approximate $\frac{16.5}{13} = 1.27\%$ chance of getting intentionally homicided over the course of one's life in Saint Pierre and Miquelon.

(The true value is that there is a 1.23% chance.)

Proof

Let $z$ be the literal percent chance of some event, $z \in [0, 100]$. (Yes, I am violating conventions for the sake of applicability here.) Assume that some event has a constant incidence of $g$ per 100,000 persons and year, and that lifespan is 75 years. Years are independent. Then, $$z = 100 \left( 1 - \left[ 1 - \frac{g}{100000} \right]^{75} \right).$$ Take the first-degree Maclaurin series of $z$, $$z \approx \frac{3}{40} x \approx \frac{x}{13}.$$

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