Statistics Question

[Dubbelosix]

Ok, imagine you had an infinite deck of cards of random faces - one of those cards has a picture of you on it.

 

The chances of course are absolutely ziltch of you ever picking out the right card - but suppose as a fluke, or miracle, you manage to pick the right card, we would say (?) the chances of you picking the right card was 1 in an infinity. 

 

Let's change the situation and the rules slightly. This time we have a second deck of cards as well as the first deck of cards. In the second deck of cards, you have an infinite amount of blank cards. In the first pack, still an infinite amount of faces. This time you are not looking for your face specifically, this time finding any face on a card will do. 

 

Picking a card, you get a face card: So...

 

1. you had an infinite amount of cards that you could have found a face on

 

2. You had an infinite amount of cards you couldn't have found a face on

 

What are the chances you would have found a card with a face on it?

Edited May 26, 2017 by Dubbelosix

[mrg]

Interesting, 006.   Regard the two decks as one deck -- of course, still infinite -- and that the face cards are arranged between blank cards by a specific interval -- one blank card, two blank cards, three blank cards, or so on.  The probability of picking a face card would be then 1/2, 1/3, 1/4, and so on.   If we didn't know they were on a specific interval, we would assume 1/2.   As we pulled more cards from the stack, we might find it varying from 1/2 over a long sequence.   Without taking a long sequence, we couldn't know what the probability is.   Even with a long sequence, we couldn't be certain that the ratio would hold over the longer run.

 

Or so I surmise.  I am not remotely an expert on such matters.

[mrg]

Well, if there's only one face card of 006 out of an infinity of face cards, the probability of selecting it limits to zero.

 

Incidentally, we could create any ratio of blank to face cards by order of selection from the two decks.  We could select 1 blank card, 1 face card; 10 blank cards, 1 face card; 100 blank cards, 1 face card; and so on -- with the corresponding declining probability of finding a face card in the combined deck.  Since we would never come to the end of it, we would never run into an imbalance issue.

[OceanBreeze]

Ok, imagine you had an infinite deck of cards of random faces - one of those cards has a picture of you on it.

 

The chances of course are absolutely ziltch of you ever picking out the right card - but suppose as a fluke, or miracle, you manage to pick the right card, we would say (?) the chances of you picking the right card was 1 in an infinity. 

 

Let's change the situation and the rules slightly. This time we have a second deck of cards as well as the first deck of cards. In the second deck of cards, you have an infinite amount of blank cards. In the first pack, still an infinite amount of faces. This time you are not looking for your face specifically, this time finding any face on a card will do. 

 

Picking a card, you get a face card: So...

 

1. you had an infinite amount of cards that you could have found a face on

 

2. You had an infinite amount of cards you couldn't have found a face on

 

What are the chances you would have found a card with a face on it?

 

Well, for one thing you cannot stack one infinity on top of another without causing an end to one and a beginning to the other, so neither can be an infinity. Therefore, the two decks must be mixed together, and in an infinite mix, no matter how it is done, the probability should average out to 50-50.

[mrg]

Yes this makes sense. 

 

Does it?  There is nothing to prevent going through a trial and finding that over the long run you, say, yank ten blank cards for each face card.   The quantity of each is still infinite; it's just a question of relative density.   If we were to postulate an infinite atmosphere and say it had multiple molecular constituents, we would not know the concentrations of the constituents on the basis of that postulate.   We'd have to sample the atmosphere to determine the ratios, and then assume the concentrations were the same where we couldn't sample it.

[mrg]

Forgive me, but ... this seems very close to saying that you are asking a question, but are not capable of assessing the answer.

[Turtle]

Ok, imagine you had an infinite deck of cards of random faces - one of those cards has a picture of you on it.

 

The chances of course are absolutely ziltch of you ever picking out the right card

No. If my face card exists there is a chance for me to pick it so the probability is not 'zilch' presuming zilch=0. I might very well pick my face on the first try.

 

- but suppose as a fluke, or miracle, you manage to pick the right card, we would say (?) the chances of you picking the right card was 1 in an infinity. 

 

Let's change the situation and the rules slightly. This time we have a second deck of cards as well as the first deck of cards. In the second deck of cards, you have an infinite amount of blank cards. In the first pack, still an infinite amount of faces. This time you are not looking for your face specifically, this time finding any face on a card will do. 

 

Picking a card, you get a face card: So...

 

1. you had an infinite amount of cards that you could have found a face on

 

2. You had an infinite amount of cards you couldn't have found a face on

 

What are the chances you would have found a card with a face on it?

As I understand it, the probability 1/∞ is not well defined so your additional questions are not well defined either. If you have no practical application/reason for the questions then there is no point pondering them.

[Turtle]

I challenge that. 

 

In my physics research, anything that exists statistically up to a certain threshold either proves something is likely to happen or it doesn't. Because we have already established the cards are infinite, the chances of you actually getting the right card must also vanish towards zero.

While probability is used in statistics, it is not statistics. Likewise, 'towards' is not 'at'.

 

If this is all just your mind twiddling, I'll leave you to it. :hammer:

[mrg]

We are meddling about with infinities and unless you know the general accord of how to address the mixing of two infinities ...

 

You can mix them any way you like.  Suppose 0 == blank, 1 == face, then we could have an infinite stack of cards like:

 

0101010101 ...

 

or 001001001001001 ...

 

or 0001000100010001 ...

 

giving probabilities of face cards of 1/2, 1/3, or 1/4, or ...

 

If you assume the mix is perfectly random, then by definition the probability of selecting a face card is 1/2,   If you don't make that assumption, you can't assess the probability.

[mrg]

it doesn't actually matter how you arrange two infinities

 

In what sense?   Obviously, if the stack is arranged:   00010001000100010001 ... there are an infinite number of 0s and 1s, but if cards are selected at random from it, the probability of getting a face card is 1/4.   Of course, as stated, we might as well assume the probability is 1/2.

[mrg]

So, this is what I recollected. How does that impact this, or doesn't it?

 

Don't know.  I would wonder:  "Doesn't matter, in what respect?" 

[mrg]

Still, imagine an infinite atmosphere that's 75% O2, 24% N2, and 1% CO2.   There are infinite quantities of all the gases, but the proportion of them is the same everywhere.

[mrg]

Sure.  Limits to zero.  Needle in infinite haystack.

[OceanBreeze]

You can mix them any way you like.  Suppose 0 == blank, 1 == face, then we could have an infinite stack of cards like:

 

0101010101 ...

 

or 001001001001001 ...

 

or 0001000100010001 ...

 

giving probabilities of face cards of 1/2, 1/3, or 1/4, or ...

 

If you assume the mix is perfectly random, then by definition the probability of selecting a face card is 1/2,   If you don't make that assumption, you can't assess the probability.

 

 

Since the problem set involves two infinite decks of cards, I think it is fair to say that the cardinality of both sets is equal. As you know, not all infinities are created equal, but in this case, that would be the assumption since the objects are the same.

 

Therefore, while you may have strings of many 0’s in the mix, there would also have to be strings of many 1’s somewhere else. Over an infinity of cards, no matter what any local arrangement may be, the odds of finding a 0 or a 1 must be equal.

 

Obviously if you designate that you are going to pick from a locality where there is a string of 0 or 1 then the above does not apply but that is a predetermined outcome (you need to know in advance where the sequence is) and nothing to do with statistics. If the point you pick from is randomly chosen, the odds are 50-50 for a 0 or a 1.

[mrg]

 As you know, not all infinities are created equal, but in this case, that would be the assumption since the objects are the same.

 

Sure.  If we assume that the combined deck is not arranged in any particular order, the odds of a 1 or 0 can be assumed to be 50:50.   Of course, by that token, the assumption of random order automatically gives the 50:50 odds.

[mrg]

Further comment:   there is an infinite sequence of every possible arrangement ( ... 01010101 ... 001001001001 ... 000100010001 ... )  in the random stack of cards -- but the odds of stumbling into one of them limits on zero.

[Turtle]

So I guess you'd like that ''real world'' example now?

 

Basically it comes down to quantum mechanics and the universal wave function. Quantum cosmology dictates that as recorded by Wolf in his book ''Parallel Universes, 1985'' that the universe had at its disposal, an infinite amount of possible start up conditions it could have chosen from (because of the wave function). 

 

I extended that to also mean, that there should be in principle also an infinite amount of possible universes that could never bare reality. These I have called the failed universes (or blank cards as they translate in the thought experiment). 

 

This was (as had been expected by other posters) irrespective of order and they are also of the same magnitude, which was key to the thought experiment itself. All that matters and what the statistics boil down to, is a selection of a specific reality, from an infinite mixed deck of possible realities, to those infinite selections that find ways to never produce the reality we see around us.

 

 

This is a hypothesis, of course. I cannot prove the same amount of possible universes that can exist is of the same magnitude as those that do not, it may turn out I may be wrong and that the failed universes are significantly less, depending on a certain constraint of fine tuning parameters, which I admit is possible. 

 

But there you have it, if you can sort out a logical statistical interpretation of those dynamics, you're doing theoretically the same selection the universe made during the initial stages of ''creation.'' 

 

Yes & thank you. While I read the cosmology posts it's not my forte and I can't offer any insight into your pursuit. Thanks for playing.