probability of infinite possibilities

[kill dank]

If something had an actual infinite number of possibilities, can any one of those possibilities be true, or happen?

Partial Example 1. Lets say you have a bag filled with an infinite number identical of marbles. If you reach into the bag, what is the possibility that you will pick one marble over another? if you have 10 marbles, you have a 1 out of 10 chance of selecting any marble. if you have 100, thats a 1 out of 100 chance, and so on and so forth. if you have an infinite number of marbles, the ratio would be 1:∞ leaving you with a 1 in infinity chance you will select ANY marble. Does that mean that mathematically it is impossible for me to choose a marble since any number compared to ∞ is equal to 0?

Partial Example 2. Let's say that there was a lottery, and there were literally an infinite number of people playing the lottery, could any 1 person ever win?
In a lottery with 10 people, each person has a 10% chance to win, with 100 people it's 1%, with 1,000 it's .1%, and so on, and so on. Is there a point where said lottery becomes un-winnable to anyone because of the probability being 0 out of ∞?

 

[Angelmax]

If something had an actual infinite number of possibilities, can any one of those possibilities be true, or happen?

Partial Example 1. Lets say you have a bag filled with an infinite number identical of marbles. If you reach into the bag, what is the possibility that you will pick one marble over another? if you have 10 marbles, you have a 1 out of 10 chance of selecting any marble. if you have 100, thats a 1 out of 100 chance, and so on and so forth. if you have an infinite number of marbles, the ratio would be 1:∞ leaving you with a 1 in infinity chance you will select ANY marble. Does that mean that mathematically it is impossible for me to choose a marble since any number compared to ∞ is equal to 0?

No, this means that you are certain to pick a marble.

Partial Example 2. Let's say that there was a lottery, and there were literally an infinite number of people playing the lottery, could any 1 person ever win?
In a lottery with 10 people, each person has a 10% chance to win, with 100 people it's 1%, with 1,000 it's .1%, and so on, and so on. Is there a point where said lottery becomes un-winnable to anyone because of the probability being 0 out of ∞?

Maybe I'm making a mistake, but surely as with your first example there is a 100% chance that someone will win.

 

If something had an actual infinite number of possibilities, can any one of those possibilities be true, or happen?

Partial Example 1. Lets say you have a bag filled with an infinite number identical of marbles. If you reach into the bag, what is the possibility that you will pick one marble over another? if you have 10 marbles, you have a 1 out of 10 chance of selecting any marble. if you have 100, thats a 1 out of 100 chance, and so on and so forth. if you have an infinite number of marbles, the ratio would be 1:∞ leaving you with a 1 in infinity chance you will select ANY marble. Does that mean that mathematically it is impossible for me to choose a marble since any number compared to ∞ is equal to 0?

The concept of probability applies only to finite sets, so the question in its conception is a fallacy.

If however, we assume there are simply a great number of marbles (and not infinite) then all this tiny ratio refers to is the probability of picking any particular marble over all others.

That is: the probability of picking the one red marble in a bag of 1E99999 black marbles is 1 in 1E99999 = ~0.

No, this means that you are certain to pick a marble.

He is certain to pick a marble because he is undertaking the act of picking a marble, not because of anything to do with the probability of selecting a particular marble.

Partial Example 2. Let's say that there was a lottery, and there were literally an infinite number of people playing the lottery, could any 1 person ever win?
In a lottery with 10 people, each person has a 10% chance to win, with 100 people it's 1%, with 1,000 it's .1%, and so on, and so on. Is there a point where said lottery becomes un-winnable to anyone because of the probability being 0 out of ∞?

It depends on the number of unbought tickets. If there are again 1E99999 tickets, only 100 of which have been purchased, then the chances of anyone winning are 1 in 1E99999 / 100, which is again practically zero.

 

[Angelmax]

The concept of probability applies only to finite sets, so the question in its conception is a fallacy.

If however, we assume there are simply a great number of marbles (and not infinite) then all this tiny ratio refers to is the probability of picking any particular marble over all others.

This is what I was trying to get at, my brain must have gone to sleep for the night. What Sythe is saying is correct, the concept of linear probability only applies to non-infinite numbers.

 

[kill dank]

The concept of probability applies only to finite sets, so the question in its conception is a fallacy.

If however, we assume there are simply a great number of marbles (and not infinite) then all this tiny ratio refers to is the probability of picking any particular marble over all others.

That is: the probability of picking the one red marble in a bag of 1E99999 black marbles is 1 in 1E99999 = ~0.




He is certain to pick a marble because he is undertaking the act of picking a marble, not because of anything to do with the probability of selecting a particular marble.

It depends on the number of unbought tickets. If there are again 1E99999 tickets, only 100 of which have been purchased, then the chances of anyone winning are 1 in 1E99999 / 100, which is again practically zero.

that makes perfect sense. i missed the whole ""The concept of probability applies only to finite sets"" part of the lesson.