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## 1 in an infinity

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Name Is Unnecessary
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### 1 in an infinity

This is a thought experiment: imagine an infinite set of blue marbles. Now add 1 red marble to it. Randomly pick a marble. What is the probability to pick the red one? Try not to mention its inapplicability as a real experiment - be hypothetical.

LuckyR
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### Re: 1 in an infinity

Not zero
"As usual... it depends."

Tamminen
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### Re: 1 in an infinity

I am not a mathematician, but I think probabilities can be calculated only with finite sets. Infinite sets are mathematical abstractions with their own curiosities, having not much to do with real phenomena.

LuckyR
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### Re: 1 in an infinity

Similarly not a mathematician, but I seem to recall that infinite concepts are dealt with routinely in that discipline (curves coming infinitely close to lines yet never touching etc). Again my memory is very imperfect, but infinity minus 1, is not infinite (is finite), yet is so close to infinity that extremely close approximations to the behavior of infinity can be made.
"As usual... it depends."

Steve3007
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### Re: 1 in an infinity

I'm going to go with zero. Is there a follow-up question?

I have one: If you randomly pick one of the infinite set of all real numbers what is the probability that it will also be one of the infinite set of natural numbers or integers? What is the probability that it will be one of the infinite set of even numbers?

Tamminen
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### Re: 1 in an infinity

Steve3007 wrote:
July 27th, 2018, 4:18 am
I'm going to go with zero.
This is the obvious answer. But, to be precise, 1/n approaches 0 as n grows without limit. And I think this is the answer. Because the concept of infinite set is problematic.

Steve3007
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### Re: 1 in an infinity

Yes, ok. I'll go with "tending towards zero" then.

chewybrian
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### Re: 1 in an infinity

Name Is Unnecessary wrote:
July 25th, 2018, 8:09 am
This is a thought experiment: imagine an infinite set of blue marbles. Now add 1 red marble to it. Randomly pick a marble. What is the probability to pick the red one? Try not to mention its inapplicability as a real experiment - be hypothetical.
Critically, you seem to imply that I add the marble, and I can only live so long and travel so far before choosing. I will say then that I can randomly choose any marble I could reach in my lifetime.

I'll say a marble is 1/2 inch, and they are in a single straight line, since I am not sharp enough to calculate the probabilities using a giant ball of marbles, a curvy line, groups of marbles shaped as life-sized Bea Arthurs, or other possibilities. I will randomly select a distance to travel in either direction, in 1/2 inch increments, including zero, and give equal weight to each possible choice.

Say I can last fifty years, and travel at 25,000 mph (the fastest speed a man has gone so far). There are about 63,500 inches in a mile, or about 127,000 marbles in a mile. So I could get as far as:

127,000 marbles per mile x 25,000 mph x 24 hours a day x 365 days a year x 50 years x 2 (for 2 directions of travel) or:

5,562,600,000,000,000 marbles from which to choose, leaving the chance of red at roughly:

.00000000000000018, or 5+1/2 quadrillion to one against.
"If determinism holds, then past events have conspired to cause me to hold this view--it is out of my control. Either I am right about free will, or it is not my fault that I am wrong."

ThomasHobbes
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### Re: 1 in an infinity

Since it is perfectly reasonable to be able to add one red ball to many blues balls, the impossibility of calculating a probability in this case is evidence that an infinite series is in comprehensible, and physically impossible.
Hypotheticals are constructed to examine logical and practical possibilities. It is absurd of you to say "Try not to mention its inapplicability as a real experiment", since hypo-thetical insists that we show what lies under the situation.

Tamminen
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### Re: 1 in an infinity

chewybrian wrote:
July 27th, 2018, 10:29 am
5,562,600,000,000,000 marbles from which to choose, leaving the chance of red at roughly:

.00000000000000018, or 5+1/2 quadrillion to one against.
If the red marble is already at a random place in the infinite row, whatever this means, the probability that it is among the first 5,562,600,000,000,000 marbles is itself zero.

chewybrian
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### Re: 1 in an infinity

Tamminen wrote:
July 27th, 2018, 1:18 pm
chewybrian wrote:
July 27th, 2018, 10:29 am
5,562,600,000,000,000 marbles from which to choose, leaving the chance of red at roughly:

.00000000000000018, or 5+1/2 quadrillion to one against.
If the red marble is already at a random place in the infinite row, whatever this means, the probability that it is among the first 5,562,600,000,000,000 marbles is itself zero.
We were instructed to 'get hypothetical', so I did. The instructions said "now add 1 red marble", I made the leap to say that I was being told to add the red marble, so *I* had to add it, meaning that I began at the location at which I added it, and I can only live so long, travel so fast...
"If determinism holds, then past events have conspired to cause me to hold this view--it is out of my control. Either I am right about free will, or it is not my fault that I am wrong."

Tamminen
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### Re: 1 in an infinity

chewybrian wrote:
July 27th, 2018, 10:29 am
I will randomly select a distance to travel in either direction, in 1/2 inch increments, including zero, and give equal weight to each possible choice.
So if you are very old, you probably select a short distance randomly within the range you think you can manage, and the probability of picking the red marble is greater than for a youngster. Some advantages for getting old if you are fond of red marbles

Fdesilva
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### Re: 1 in an infinity

If there is one red marble in an infinite set of blue marble the probability of picking the red marble is zero. Basically it is impossible to pick the red marble.

RJG
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### Re: 1 in an infinity

Name Is Unnecessary wrote:This is a thought experiment: imagine an infinite set of blue marbles. Now add 1 red marble to it. Randomly pick a marble. What is the probability to pick the red one?
Simple -- an "infinity-to-one" odds.

Intellectual_Savnot
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### Re: 1 in an infinity

The possibilty ratio is exactly .0(repeated)1/1 or .0000000.....1/1