The way you would do this statistical calculation is to calculate the chance of escaping after N trials, whatever a trial is in this case. Those are statistically independent events, and thus the probability compounds exponentially:

(1 - 0.137)^N = P, **where P is the probability that you would still be free after N trials.[b/]**

It is not clear what "per year" means. Either 14% of auto thieves are arrested, period, or 14% of auto thieves are arrested within one year, or 14% of outstanding auto thefts are solved per year.

Admittedly, statistics are my weakest math skill. I have only taken one formal statistics course. Neither of the formulas we offered are correct.

I can show you that the formula you offered is not applicable by showing you an example of it not producing a coherent result.

If I use N=10 years the result is 0.229

If I use N=20 years the result is 0.05

That doesn't make any sense.

An individual is NOT more likely to be free (0.05) after 20 years of commitment to auto thefts as compared to after 10 years (0.229).

My source for the 13.7% figure:

Clearances
Perhaps, the probability of P(A) after N years is 1-[P(B)]^N ??

So after 6 years there is a 59% chance the car thief would be caught.

After 12 years there would be an 83% chance the thief would be caught. This assumes the thief is active every years.