Probability
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20-03-2013, 11:11 AM
RE: Probability
(20-03-2013 07:43 AM)pgrimes15 Wrote:  
(20-03-2013 12:47 AM)Heywood Jahblome Wrote:  Grimesy, you are in error. An is always greater than 0 by definition. Think about it this way, An is n white marble draws in a row. P(An) is the probability of n white marbles in a row. As long as it is logically possible to draw a white P(An) is greater than 0 for any n. Is the probability of drawing 5 white marbles in a row greater than 0? Or 10 white marbles in a row? Or a billion? Yes, if the composition of the bin is unknown to you then the assumption that it is logically possible to draw another white marble is reasonable.

Also regarding the .25. You are wrong about that too. It is true that the probability of flipping 3 heads in a row is .125. It would be true that drawing 3 white marbles in a row has a probability of .125 but only if drawing a white marble itself had a probability of .5. However you don't know anything about the composition of the bin. In the example you are told there ar 3 marbles in the bin, but no information is given to you regarding the distribution of colors. So you can't


say there is a .5 probability of drawing a white. The only reasonable assumption is that all distributions are equally likely. In fac t th e example says that. Since there are only 4 possible distributions of the colors, and each distribution is equally likely, it stands to reason that each distribution has a .25 probability.

This feels a bit like pigeon chess . Mathematical probability cannot be applied to an infinite series of unknowns like your white/black ball scenario. Your assertion that P(X) decreases as n increases cannot be justified mathematically
Is this the heart of your strategy ? Get established that the probability of a black ball (miracle?) decreases over time, then suddenly invert this to "prove" the probability of God existing increases over time .

Regards

Grimesy

I agree it does feel like pigeon chess. P(X|An) means the probability of X given An. Remember that An is a condition and that we talking about the probability of X only under the condition An. If a black marble is drawn the proof does not apply. Do you agree now that it was silly of you to claim that P(An) is 0 if a black marble is drawn?
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20-03-2013, 11:20 AM
Re: Probability
The probabilities were calculated off of the observations and do not indicate what the number of colors actually is within the bucket, only the number of colors drawn.

And probabilities are our estimates of our observations and must necessarily be estimated as they always have some associated variance.

Your answer of "5 or more" means infinity, and there was a finite number of colors. This is the point. Observations only indicate what we observe and there could still be some infinite number of colors in the bucket. Even when there isn't, we can't assert that based on our observations.

Now, let's say we make a technological breakthrough that changes the frequency at which we start drawing out the non-white colors such that our 4 colors now come out in equal proportions. Were our first observations wrong? Were the calculated probabilities wrong? Is our current method wrong?
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20-03-2013, 11:24 AM
Re: Probability
It should also be pointed out that probabilities calculated from observations are estimates but probabilities calculated mathematically from known variations in the system are not estimates.

Ergo, knowing that a coin has 2 sides leads to a probability of 50/50

But calculating a probability off of some number of trials will give something close to 50/50 (assuming enough trials) with a variance that means this probability is an estimate.
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20-03-2013, 12:01 PM
RE: Probability
(20-03-2013 11:20 AM)TheBeardedDude Wrote:  The probabilities were calculated off of the observations and do not indicate what the number of colors actually is within the bucket, only the number of colors drawn.

And probabilities are our estimates of our observations and must necessarily be estimated as they always have some associated variance.

Your answer of "5 or more" means infinity, and there was a finite number of colors. This is the point. Observations only indicate what we observe and there could still be some infinite number of colors in the bucket. Even when there isn't, we can't assert that based on our observations.

Now, let's say we make a technological breakthrough that changes the frequency at which we start drawing out the non-white colors such that our 4 colors now come out in equal proportions. Were our first observations wrong? Were the calculated probabilities wrong? Is our current method wrong?

5 or more does not mean infinity. It means 5(which is finite) or some number(all numbers are finite) greater than 5.

To answer your questions, our first observations where not wrong(unless the observer is color blind or something). Were are estimates wrong? Sure but the method is sound. Just because it appeared likely there were only 4 colors doesn't preclude the chance of an outlier. I never claimed there could not be outliers.
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20-03-2013, 12:09 PM
RE: Probability
(20-03-2013 11:24 AM)TheBeardedDude Wrote:  It should also be pointed out that probabilities calculated from observations are estimates but probabilities calculated mathematically from known variations in the system are not estimates.

Ergo, knowing that a coin has 2 sides leads to a probability of 50/50

But calculating a probability off of some number of trials will give something close to 50/50 (assuming enough trials) with a variance that means this probability is an estimate.
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Only if it is assumed that the results of a flip are random and the coin is true. Incidentally there was a study done which claims it is more likely a coin will land on the same side it started.
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20-03-2013, 12:59 PM
RE: Probability
Really? We're still here?

At some point, we all have to realize that BlowJob is not the least bit interested in learning about probability. He's trolling, stirring up trouble, and laughing at how much energy everyone is wasting trying to educate his sorry ass. If he cared at all, he would have clued in by now, and surely he did, but that's not why he's keeping this thread alive, arguing in circles, ignoring everyone's rebuttals.

"Whores perform the same function as priests, but far more thoroughly." - Robert A. Heinlein
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20-03-2013, 01:07 PM
Re: Probability
This does appear to be nothing more than a circlejerk. Especially when examples are given for coin flips and the qualifier of "If it is a true coin" comes out.

Go grab a stats book.
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20-03-2013, 01:34 PM
RE: Probability
(20-03-2013 12:59 PM)Aseptic Skeptic Wrote:  Really? We're still here?

At some point, we all have to realize that BlowJob is not the least bit interested in learning about probability. He's trolling, stirring up trouble, and laughing at how much energy everyone is wasting trying to educate his sorry ass. If he cared at all, he would have clued in by now, and surely he did, but that's not why he's keeping this thread alive, arguing in circles, ignoring everyone's rebuttals.

I forgive you for spreading these lies about me.
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20-03-2013, 01:38 PM
RE: Probability
(20-03-2013 01:07 PM)TheBeardedDude Wrote:  Go grab a stats book.

That's good advice you would do well to follow.
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20-03-2013, 01:55 PM
Re: Probability
I have a few. Had to have them for Intro to stats, multivariate statistics, and ANOVA and experimental design.
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