### The Math Behind The “Once In A Century” Statement

Lynne Kiesling

Robert Ayres has very kindly done the math to show why Posner’s statement in the WSJ that I referred to on Tuesday is correct, but agrees with me that he could have said it better. From the email he sent me:

If his “later” means “later in the century”, then
the question is

in the first decade or the following ninety years?

Expanding, the chances of the (first) once-per-hundred years event
occurring in the first decade is 1 – 0.99^10 = 0.095
(One minus the chance it occurs in none of the ten years.)

The chances of it occurring later, but in the next 90 years is
(1 – 0.095 ) * ( 1 – 0.99^90 ) = 0.539

And if “later” means “amytime later”, then the chances of that
are the same as the chances that it does not occur during the first
decade, since any event with some probability will occur eventually:

The chance that the first occurrence occurs sometime after the first
decade is 0.99^10 = 0.905.

Excellent; full marks! And as a lazy applied mathematician, I appreciate the heavy lifting he’s done.