Data Intelligence, Business Analytics
Your chance of having a car accident in the next 25,000 miles is independent of how many car accidents you had during the last 25,000 miles, or even during the last 300,000 miles for that matter.
In other words, the car accident process is a memory-less stochastic process. You'd think that if you have been driving for 15 years without a single car accident, the chance of having a car crash during your next trip is much higher than for a good driver who already had 2 car crashes over the last 15 years: you think that you have been very lucky so far, and that your luck won't last forever. Indeed, this is not the case - car crashes (for good drivers as well as for bad drivers) very closely follow a memory-less stochastic Poisson process: with low intensity for good drivers, and high intensity for bad drivers. The fact that you did not have a car crash over the last 15 years does not mean that you are more likely to have one tomorrow, and the other way around. This fact is very easy to prove, either based on car crash data, or via car driving simulations.
On the other side, it is also very easy to prove that the more you drive, the more you risk having a car crash. Indeed, the expected number of car crashes you will have in your lifetime - given how good or bad a driver you are - is proportional to the number of miles that you will drive.
How do you explain this paradox?