Another way of thinking about stochastic processes

 

Imagine a dice game where you win a chocolate if you throw a double six. There is a fixed chance of throwing the double six but the more times you throw the dice, the more likely you are to win. However, the prize is the same no matter how many times you have to throw the dice. So the longer the time, the more likely the effect, but the effect is the same regardless of how long it takes.