Do Probabilities Always Approach Extremes at Infinity?

[Gelsamel Epsilon]

Is it just me or do all high probabilities dwindle to nothing as time approaches infinity and all small probabilities increase to 1 as time approaches infinity?

 

[StatusX]

Have any examples?

 

[quasar987]

Your question is vague but here's a kind of counter exemple:

Each of N girls have a ball with a number on it (1 to N). They all throw their ball in an urn and take one at random. What is the probability that no girl take her own ball? Intuitively, it would seem that as N goes to infinity, the probability that NO girl ever taker her ball is zero. But this probability goes to 1/e as N-->oo, while it is quite large for small N.

This probability is not time dependant, but is this kind of what you were talking about?

 

[matt grime]

Is it just me or do all high probabilities dwindle to nothing as time approaches infinity and all small probabilities increase to 1 as time approaches infinity?

It is you (unless you deign to tell us in what way you think *all* probabilities are in any way dependent on time,since most of them are not: the probabiliy I get deal a straight flush in poker is in no way time dependent, for example.)

 

[Gelsamel Epsilon]

Mmm well the examples I thought of were like, the probability that Earth is here tomorrow when I wake up. I'd say that is extremely close to 100%, but as time tends towards infinity the chance the Earth still exists dwindles to nothing. Similarly the chance that an asteroid hits Earth and destroys it in the next 2 seconds is so close to 0 it isn't funny, but as time tends towards infinity it is certain that Earth will be hit by an asteroid (assuming Earth is there that long).

And if you were playing poker for an infinite amount of years the chance that you get a royal flush is low when you first start playing but by the time that time reaches infinity you're almost certain to have gotten a royal flush by then.

 

[matt grime]

1. don't confuse and with or (the Earth surviving tomorrow, and the next day and the next day.. versus being hit by a meteor tomorrow or the next day or the day after that...)

2. and don't say 'when time reaches infinity'

 

[Gelsamel Epsilon]

1. don't confuse and with or (the Earth surviving tomorrow, and the next day and the next day.. versus being hit by a meteor tomorrow or the next day or the day after that...)

2. and don't say 'when time reaches infinity'

I don't get anything from this, it just sounds like semantics.

 

[matt grime]

Since you got the semantics wrong, why not start with explaining the semantics of it?

1. You're comparing apples and oranges: one is an 'and' the other an 'or' statement. There is a difference between asking X and Y and Z happen, and asking that X or Y or Z happen and has nothing to do with the probabilities of X, Y, or Z being large or small (relatively).2. Don't say when time reaches infinity.

 

[StatusX]

Say you roll a die a 1000 times. The probability of getting 3 every time is (1/6)^1000, which is very small. This is the probability of getting a 3 and a 3 and a 3, and so on. On the other hand, the probability of getting no 3's is (5/6)^1000, which is also very small. Then the chance of getting a 3 at least once is just the 1 minus the chance of never getting a 3, which is 1-(5/6)^1000, and which is very close to 1. This is the probability of getting a 3 or a 3 or a 3, and so on. Do you understand this difference? Note also that you can replace 1/6 by any probability between 0 and 1 and you'll get the same result, ie, that the chance of something happening every time for a large number of times is very small, while the chance of it happening at least once out of a large number of times is very close to 1.

 

[Gelsamel Epsilon]

Ok I see, thanks for explaining that, I hate probability, the only math I don't really like.