Thinking about stochastic and non-stochastic

I've been thinking about stochastic and non-stochastic processes in radiation health issues. Stochastic basically means down to chance. In stochastic processes, the effect is independent of the dose received but the bigger the dose, the higher the probability of receiving that effect. I started thinking about driving. Careful drivers are unlikely to have an accident - there is a low probability. But obviously, the more hours you drive, the more likely to have an accident. The insurance companies know this - that's why the higher the mileage, the higher the premium. But driving a higher mileage doesn't make the damage worse in any given crash. That's why I think it is a stochastic process. Now think about reckless driving. If you deliberately drive at higher and higher speeds, then there will be a direct link between the speed and the severity of the accident. This is a non-stochastic effect.