Chance of Identical Numbers in Infinite Series

[shmoe]

I think that's an ugly abuse of the probability 1.
You can't find probabilities that are larger than 1, but an event can SURELY be more certain than just "almost surely", if you see what I mean.

Things can also "surely" happen. Consider the uniform distribution on the unit interval [0,1]. You will "almost surely" pick an irrational number. However, you will "surely" pick a real number.

You might want to look into measure theory if you want to try to understand the finer points behind probability theory. This is the stuff that they won't bother teaching your engineering stats class, but is really needed if you want to learn some rigorous probability and not just how to apply various distributions to bolts coming off an assembly line.

 

[-Job-]

Discrete & Continuous random variables have different contexts. Discrete random variables coincide more with experience because we don't generally deal with infinite sample spaces in real life. With discrete random variables we assign probability 0 to events that we suppose will not happen, so it's only a discrepancy if we don't keep in mind that the context is different, so things have different meanings. Any time we are dealing with continuous random variables we should be aware that probability 0 doesn't mean the outcome is impossible, only that it is so small that it is irrelevant. Mostly a semantics issue.

 

[wcemichael]

The answer to your questions is, YES. A chance is still a chance, even if it's a showball's chance in hell

 

[SW VandeCarr]

Ok I am not sure if this is where this thread should go, but anyway.

My question is this:
if we have an infinite series of numbers (or apples, or whatever) and we choose one at random, and then choose another at random, is there a chance that the two will be the same? I mean, is a 1 in infinity chance a chance at all?

The answer to your questions is, YES. A chance is still a chance, even if it's a showball's chance in hell

The answer is the same as it was over 5 years ago. It is possible with a probability of zero. (That's not a contradiction).