Is there a probabilistic or scientific argument that reasons "the longer you've been waiting, the longer you can expect to wait?"
I'll start with a disclaimer: I don't know if the statement exists or even if it's correct. If it is, I don't know what it would be called. On the other hand, something suggests to me that it would come from queueing theory
. I can also accept that this is nothing and I'm completely crazy.
I can't think of a good example, so please bear with me, especially the geologists in the room. Let's suppose we have volcanoes A and B. Volcano A erupted a little over a month ago, and volcano B's most recent eruption was just over three hundred years ago. One argument is that volcano B is long overdue for an eruption, so B is upcoming. This argument though, suggests that we should expect to wait even longer for B, and concludes that A is upcoming.
One of the conditions for this argument to work is if we ignore history. If we know that B erupts every three hundred years or so, and that A erupts once per millennium, then the argument shouldn't apply.
So, these are the questions to be answered:
1. First and foremost, is this even correct?
2. If correct, when can it be applied, and when can it not?
3. If correct, is it better known with a proper name?
4. Is there a prototypical example that demonstrates this clearer?
Thanks in advance!