Understanding Statistical Probability: The Mistake of Overestimating Rare Events

[Probabil1ty]

I want to know the name of one little phenomena to learn more. I don't know how to explain it clearly, so please try to understand what i am trying to know.

The problem is: When you find a very low probability event you think about it like some kind of miracle, but you did not expected any kind of event, so this is not and question of math.

EXAMPLE(imagine a normal life situation): you standing on a street and doing nothing(waiting a friend) and you see a car with a vehicle registration plate with number 111, after a couple of minutes you see a car with number 112. And you think "O my god ! wow ! the probability of seeing those two registration plates is like one to million !" But you were not making an experiment on observing registration plates. You were not expected to see that numbers. Event has already happened and after that you made this conclusion. So this is completely wrong to say that it was kind a miracle and one to million probability.

So my question is: what the name of that mistake? I think this is an interesting topic and want to learn more.
Thanks

 

[frustr8photon]

this is simply a poorly run counting experiment. that particular event (seeing 111 then 112) does indeed have a probability of something like one in a million. But the probability of seeing any two numbers that are very alike, for example (n,p,m,) then (n,p,m+1), is much, much higher than one in a million.

if you really want to learn more about this mathematically, go ahead and calculate the probabilities of finding such events. that would be interesting to see.