Probability
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12-03-2013, 02:11 AM
RE: Probability
(12-03-2013 02:00 AM)Heywood Jahblome Wrote:  
(12-03-2013 01:51 AM)Aseptic Skeptic Wrote:  No, it doesn't change the probability whatsoever. Look up the word. The probability of drawing another white marble is exactly a function of dividing the number of white marbles by the total number of marbles.

If the entire barrel is nothing but white marbles, then the probability of the next one (or of them all) being white is 100% (or 1, if you prefer).

If the entire barrel is NOT only white, then the probability of the next one being white is #white/#total, and the probability of the entire barrel being nothing but white marbles is 0% (or 0).


No, your question is poorly worded and your examples prove conclusively that you have no idea what probability means. No wonder you're gullible enough to be a theist and believe in invisible magical men manipulating the universe - it's clear that you think that merely wanting something or guessing something or believing something can actually affect what that something is...

(In case that's not clear, what I mean is, guessing that the barrel is all white, or believing that the barrel is all white, or wanting the barrel to be all white, doesn't actually make it all white, nor does it increase the probability that it will be all white - it's only an expression of your poor judgment, not of probability).
Instead of showing my example or the mathematical proof to be fatally flawed, you make another straw man argument.
You never answered my question in theother thread, so I will repeat it here:

I don't understand your notation. If X is the probability that all the marbles are white, then

P(X | An)=the conditional probability of the probability that all the marbles are white, given that the first n marbeles are white.
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12-03-2013, 02:33 AM
RE: Probability
(12-03-2013 02:11 AM)Jakel Wrote:  You never answered my question in theother thread, so I will repeat it here:

I don't understand your notation. If X is the probability that all the marbles are white, then

P(X | An)=the conditional probability of the probability that all the marbles are white, given that the first n marbeles are white.

Yes it means the probability of something given something.

P(X | An) translates into common language as..

The probability that all marbles in the bin are white given n observations of white marbles being drawn from the bin with no observations of other colored marbles being drawn from the bin.
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12-03-2013, 02:42 AM
RE: Probability
(12-03-2013 02:33 AM)Heywood Jahblome Wrote:  
(12-03-2013 02:11 AM)Jakel Wrote:  You never answered my question in theother thread, so I will repeat it here:

I don't understand your notation. If X is the probability that all the marbles are white, then

P(X | An)=the conditional probability of the probability that all the marbles are white, given that the first n marbles are white.

Yes it means the probability of something given something.

P(X | An) translates into common language as..

The probability that all marbles in the bin are white given n observations of white marbles being drawn from the bin with no observations of other colored marbles being drawn from the bin.
No. This is exactly my point. P(X | An) does not mean what you think it means, when you define X as you do.
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12-03-2013, 02:58 AM (This post was last modified: 12-03-2013 03:19 AM by Heywood Jahblome.)
RE: Probability
(12-03-2013 02:42 AM)Jakel Wrote:  
(12-03-2013 02:33 AM)Heywood Jahblome Wrote:  Yes it means the probability of something given something.

P(X | An) translates into common language as..

The probability that all marbles in the bin are white given n observations of white marbles being drawn from the bin with no observations of other colored marbles being drawn from the bin.
No. This is exactly my point. P(X | An) does not mean what you think it means, when you define X as you do.
P(X | A) means in common language, the probability of X given that A has already occurred. If you think it means something else then you are incorrect.
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12-03-2013, 03:22 AM
RE: Probability
(09-03-2013 01:50 PM)Heywood Jahblome Wrote:  This is more than the mind creating some pattern. Observing only white marbles does increase the chance that all the marbles are white.

Let X = the probability that all the marbles are white.
Let An = n observations of white marbles without ever observing a non white marble.

Assume that for all n, P(X | An) > 0 and P(An+1 | An) < 1.

we then have

P(X & An+1 | An) = P(X | An)P(An+1 | X & An)= P(X | An).

we also have

P(X & An+1 | An) = P(An+1 | An)P(X | An+1 & An)= P(An+1 | An)P(X | An+1).

Combining these give us

P(X | An) = P(An+1 | An)P(X | An+1) < P(X | An+1).

Which is another way of saying, P(X | An) is an increasing function of n.

Its important to remember that just observing white marbles does not prove there are no black marbles. All it allows you to say is that it is now more likley(then it was before), that there are no black marbles.
Could you please explain it better? I would like to understand your proof but for now it's not clear to me.

Your sample space (call it Omega) is undefined, right? This seems already confusing to me...

First of all, is it finite, infinite or even that is unknown?

Second, could you please define the events you are considering? First you talk about probabilities, then you take the probability of your probabilities Confused

A_n seems to be: "first n marbles extracted are all white", am I correct?

What is X?

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12-03-2013, 03:34 AM
RE: Probability
(12-03-2013 03:22 AM)Kreuzfel Wrote:  
(09-03-2013 01:50 PM)Heywood Jahblome Wrote:  This is more than the mind creating some pattern. Observing only white marbles does increase the chance that all the marbles are white.

Let X = the probability that all the marbles are white.
Let An = n observations of white marbles without ever observing a non white marble.

Assume that for all n, P(X | An) > 0 and P(An+1 | An) < 1.

we then have

P(X & An+1 | An) = P(X | An)P(An+1 | X & An)= P(X | An).

we also have

P(X & An+1 | An) = P(An+1 | An)P(X | An+1 & An)= P(An+1 | An)P(X | An+1).

Combining these give us

P(X | An) = P(An+1 | An)P(X | An+1) < P(X | An+1).

Which is another way of saying, P(X | An) is an increasing function of n.

Its important to remember that just observing white marbles does not prove there are no black marbles. All it allows you to say is that it is now more likley(then it was before), that there are no black marbles.
Could you please explain it better? I would like to understand your proof but for now it's not clear to me.

Your sample space (call it Omega) is undefined, right? This seems already confusing to me...

First of all, is it finite, infinite or even that is unknown?

Second, could you please define the events you are considering? First you talk about probabilities, then you take the probability of your probabilities Confused

A_n seems to be: "first n marbles extracted are all white", am I correct?

What is X?

X is the probability that all the marbles in the bin are white.
You are correct. An is n white marbles drawn without ever observing a black one(let black mean any other color).
The proof works for any finite number of marbles.
sample space {all marbles in the bin are white, marbles in the bin are of mixed color}
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12-03-2013, 03:38 AM
RE: Probability
If X is the probability that all the marbles in the bin are white, what is the meaning of P(X|A_n)?

We walk by faith, not by sight. Angel
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12-03-2013, 03:53 AM
RE: Probability
(12-03-2013 02:58 AM)Heywood Jahblome Wrote:  
(12-03-2013 02:42 AM)Jakel Wrote:  No. This is exactly my point. P(X | An) does not mean what you think it means, when you define X as you do.
P(X | A) means in common language, the probability of X given that A has already occurred. If you think it means something else then you are incorrect.
Yes this is what it means. How can you not see that if
X=the probability that all the marbles is white
that P(X | A) does not mean what you think it means Dodgy I can only conclude that you did not make this "proof" yourself.
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12-03-2013, 03:53 AM
RE: Probability
(12-03-2013 03:38 AM)Kreuzfel Wrote:  If X is the probability that all the marbles in the bin are white, what is the meaning of P(X|A_n)?
Thank you! At least I'm not the only one confused here Huh
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12-03-2013, 04:11 AM
RE: Probability
Yes, he did a mistake. Jahblome, maybe you should review you "proof". I am not saying you are wrong, maybe you are right, I don't know, but your proof is invalid. I would suggest you to define carefully the things you are working on and then try to deduce something meaningful.

We walk by faith, not by sight. Angel
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