I've been annoyed lately by some theory of mine that looks a bit like those mathematical paradoxes presented throught history, and I would like your opinions. I'm pretty sure that I'm making a mistake somewhere in my thinking, but I can't realize where..Anyway, here goes..
Let's say that I want to predict the probability to be in an airplane accident. Let's suppose that statistics say that 1 out of 100 planes flying will crash. That means that if I am on a plane, I have 1% chance to go down. Now, if I fly 100 consecutive times and I still haven't crashed, that actually changes the statistic probabilities, right? after 110 safe trips the accident probaility will be 1 in 110, after 150 it will be 1 in 150 and so on.
BUT
Since logic says that eventually a plane will crash, isn't it so that with every trip I would, at the same time, increase actually my probabilities to be in an accident? What's true? Do chances say that it's less likely to happen, or that it's more likely to happen?