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1 in an infinity

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1 in an infinity
 LuckyR
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Re: 1 in an infinity
 LuckyR
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Re: 1 in an infinity

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Re: 1 in an infinity
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?

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Re: 1 in an infinity
 chewybrian
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Re: 1 in an infinity
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.Name Is Unnecessary wrote: ↑July 25th, 2018, 8:09 amThis 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.
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 lifesized 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.
 ThomasHobbes
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Re: 1 in an infinity
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 hypothetical insists that we show what lies under the situation.

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Re: 1 in an infinity
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 wrote: ↑July 27th, 2018, 10:29 am5,562,600,000,000,000 marbles from which to choose, leaving the chance of red at roughly:
.00000000000000018, or 5+1/2 quadrillion to one against.
 chewybrian
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Re: 1 in an infinity
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...Tamminen wrote: ↑July 27th, 2018, 1:18 pmIf 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 wrote: ↑July 27th, 2018, 10:29 am5,562,600,000,000,000 marbles from which to choose, leaving the chance of red at roughly:
.00000000000000018, or 5+1/2 quadrillion to one against.

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Re: 1 in an infinity
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 marbleschewybrian wrote: ↑July 27th, 2018, 10:29 amI 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.

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Re: 1 in an infinity
 RJG
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Re: 1 in an infinity
Simple  an "infinitytoone" odds.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?
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