Probability
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18-03-2013, 04:15 PM
RE: Probability

So as long as there isn't an infinite number of marbles then by removing any marble of any color reduces the probability of that colored marble being drawn again? Is this what you are saying?

(I think Chas said this differently: If there are any black balls, then each time you draw only white balls, it is a less and less likely event. But that's really all you can say. If that's all you are trying to say, fine.


So where are you going with this? This is more convoluted than the TV show "Lost"

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
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19-03-2013, 12:59 AM (This post was last modified: 19-03-2013 01:12 AM by Heywood Jahblome.)
RE: Probability
(18-03-2013 03:21 PM)pgrimes15 Wrote:  
(18-03-2013 01:13 PM)Heywood Jahblome Wrote:  No.....remember what An is....I bolded it for you


Sorry . . bit confused


what is P(An) or P(X) ?

X is there are no black marbles(and here black means any color(s) other than white).
P(X) is the probability of X

An is n observations of white marbles while never observing a black one.
P(An) is the probability of An.

If you draw a black marble P(X) = 0. P(An) is always going to be greater than 0 because by definition at least one white marble is observed and black ones never are observed.
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19-03-2013, 01:23 AM
RE: Probability
(18-03-2013 01:52 PM)Chas Wrote:  
(18-03-2013 01:34 PM)Heywood Jahblome Wrote:  So you are saying my perception of the quantitative description of the likely occurrence of a particular event is changing?

That makes no sense Chas.

What makes sense is my quantatative description of the likely occurrence of a particular event is changing.
No, your qualitative perception of the quantitative facts is changing. You are basing your argument on too little information.

You don't know what the distribution is, so you can't tell what your samples mean. The more white balls you draw, the more likely you think it is that there is a preponderance of white balls.

If there are any black balls, then each time you draw only white balls, it is a less and less likely event. But that's really all you can say. If that's all you are trying to say, fine.

What's changing is your argument why I am wrong. First it included "probability" and when I showed by substituting "probability" with its definition that your argument was nonsense, you take probability out altogether.

And I never claimed you drawing only white marbles meant there was a preponderance of white marbles. I only claim that the likelyhood of there only being white marbles increases with ever draw of a white marble while not drawing a black one.
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19-03-2013, 03:09 AM
RE: Probability
(18-03-2013 04:15 PM)Full Circle Wrote:  
(18-03-2013 12:00 PM)Heywood Jahblome Wrote:  

So as long as there isn't an infinite number of marbles then by removing any marble of any color reduces the probability of that colored marble being drawn again? Is this what you are saying?

(I think Chas said this differently: If there are any black balls, then each time you draw only white balls, it is a less and less likely event. But that's really all you can say. If that's all you are trying to say, fine.


So where are you going with this? This is more convoluted than the TV show "Lost"

The probability of flipping a true coin and have it land on heads ten times in a row is .0009765625.
Now suppose your first flip comes up heads, what is the probability that you will have ten flips in a row that turn out heads. Well since you only need nine more heads in row to make a total of ten flips in row, the probability is now .001953125. After another heads the probability of ten heads in a row increases to .00390625. After 9 heads in a row the probability of flipping ten heads in row has increases to .5. You see each time you flip a heads without ever flipping a tails, you increase the probability that all ten flips will be heads.

Now Vosur and Chas would claim that the above example isn't analogous to the marble problem. They would say that in the above example you know how many flips in a row you need to make to succeed. If we were trying to calculate success, then yes, we would need to know that. However we aren't trying to calculate success but rather show that each time you flip a coin and it turns up heads it increases the probability you will flip ten heads in a row. This coin flip example works for any number of flips in a row. So we can say that each time you flip a coin it increases the probability you will flip X heads in a row.

Vosur and Chas would probably say that this coin flip example still isn't analogous because we know the probability of flipping a heads is .5. Now if we are trying to calculate the probability of flipping X heads in a row that would be important. However we are not trying to calculate the probability of flipping X heads in a row but rather show that each time you flip a heads you increase the probability that you will flip X heads in a row. With a true coin the probability of flipping a heads is .5. However what if the coin is not true? What if we don't know the probability of flipping a heads? It doesn't matter because as long as the probability of flipping a heads is greater than 0, we can say that for every flip that comes up heads we increase the probability that we will flip X heads in a row.

Try it. Assume the coin isn't true. The probability of flipping X heads in a row increases with each coin flip which results in heads(and no flips resulting in tails) given the probability of flipping a heads is Y. Put in any positive quantities you want for X and Y and the probability of X heads in a row always increases with each flip which results in a heads without ever observing a tails.
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19-03-2013, 05:06 AM
RE: Probability
(19-03-2013 03:09 AM)Heywood Jahblome Wrote:  
(18-03-2013 04:15 PM)Full Circle Wrote:  So as long as there isn't an infinite number of marbles then by removing any marble of any color reduces the probability of that colored marble being drawn again? Is this what you are saying?

(I think Chas said this differently: If there are any black balls, then each time you draw only white balls, it is a less and less likely event. But that's really all you can say. If that's all you are trying to say, fine.


So where are you going with this? This is more convoluted than the TV show "Lost"

The probability of flipping a true coin and have it land on heads ten times in a row is .0009765625.
Now suppose your first flip comes up heads, what is the probability that you will have ten flips in a row that turn out heads. Well since you only need nine more heads in row to make a total of ten flips in row, the probability is now .001953125. After another heads the probability of ten heads in a row increases to .00390625. After 9 heads in a row the probability of flipping ten heads in row has increases to .5. You see each time you flip a heads without ever flipping a tails, you increase the probability that all ten flips will be heads.

Now Vosur and Chas would claim that the above example isn't analogous to the marble problem. They would say that in the above example you know how many flips in a row you need to make to succeed. If we were trying to calculate success, then yes, we would need to know that. However we aren't trying to calculate success but rather show that each time you flip a coin and it turns up heads it increases the probability you will flip ten heads in a row. This coin flip example works for any number of flips in a row. So we can say that each time you flip a coin it increases the probability you will flip X heads in a row.

Vosur and Chas would probably say that this coin flip example still isn't analogous because we know the probability of flipping a heads is .5. Now if we are trying to calculate the probability of flipping X heads in a row that would be important. However we are not trying to calculate the probability of flipping X heads in a row but rather show that each time you flip a heads you increase the probability that you will flip X heads in a row. With a true coin the probability of flipping a heads is .5. However what if the coin is not true? What if we don't know the probability of flipping a heads? It doesn't matter because as long as the probability of flipping a heads is greater than 0, we can say that for every flip that comes up heads we increase the probability that we will flip X heads in a row.

Try it. Assume the coin isn't true. The probability of flipping X heads in a row increases with each coin flip which results in heads(and no flips resulting in tails) given the probability of flipping a heads is Y. Put in any positive quantities you want for X and Y and the probability of X heads in a row always increases with each flip which results in a heads without ever observing a tails.
I ask a simple question about marbles and you give me this ↑ about flipping coins? You funny.

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
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19-03-2013, 05:14 AM
Re: Probability
Probabilities don't accumulate.
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19-03-2013, 05:27 AM
RE: Probability
(19-03-2013 05:14 AM)TheBeardedDude Wrote:  Probabilities don't accumulate.

This isn't accumulation but rather increase or decrease based on new information.
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19-03-2013, 05:45 AM
RE: Probability
(19-03-2013 05:06 AM)Full Circle Wrote:  
(19-03-2013 03:09 AM)Heywood Jahblome Wrote:  The probability of flipping a true coin and have it land on heads ten times in a row is .0009765625.
Now suppose your first flip comes up heads, what is the probability that you will have ten flips in a row that turn out heads. Well since you only need nine more heads in row to make a total of ten flips in row, the probability is now .001953125. After another heads the probability of ten heads in a row increases to .00390625. After 9 heads in a row the probability of flipping ten heads in row has increases to .5. You see each time you flip a heads without ever flipping a tails, you increase the probability that all ten flips will be heads.

Now Vosur and Chas would claim that the above example isn't analogous to the marble problem. They would say that in the above example you know how many flips in a row you need to make to succeed. If we were trying to calculate success, then yes, we would need to know that. However we aren't trying to calculate success but rather show that each time you flip a coin and it turns up heads it increases the probability you will flip ten heads in a row. This coin flip example works for any number of flips in a row. So we can say that each time you flip a coin it increases the probability you will flip X heads in a row.

Vosur and Chas would probably say that this coin flip example still isn't analogous because we know the probability of flipping a heads is .5. Now if we are trying to calculate the probability of flipping X heads in a row that would be important. However we are not trying to calculate the probability of flipping X heads in a row but rather show that each time you flip a heads you increase the probability that you will flip X heads in a row. With a true coin the probability of flipping a heads is .5. However what if the coin is not true? What if we don't know the probability of flipping a heads? It doesn't matter because as long as the probability of flipping a heads is greater than 0, we can say that for every flip that comes up heads we increase the probability that we will flip X heads in a row.

Try it. Assume the coin isn't true. The probability of flipping X heads in a row increases with each coin flip which results in heads(and no flips resulting in tails) given the probability of flipping a heads is Y. Put in any positive quantities you want for X and Y and the probability of X heads in a row always increases with each flip which results in a heads without ever observing a tails.
I ask a simple question about marbles and you give me this ↑ about flipping coins? You funny.

If you want, I will show that what applies to coin flips applies to marbles as well.
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19-03-2013, 05:54 AM
RE: Probability
(19-03-2013 12:59 AM)Heywood Jahblome Wrote:  
(18-03-2013 03:21 PM)pgrimes15 Wrote:  Sorry . . bit confused


what is P(An) or P(X) ?


X is there are no black marbles(and here black means any color(s) other than white).
P(X) is the probability of X

An is n observations of white marbles while never observing a black one.
P(An) is the probability of An.

If you draw a black marble P(X) = 0. P(An) is always going to be greater than 0 because by definition at least one white marble is observed and black ones never are observed.


If you draw a black marble, then P(An) also equals 0.

Therefore the expression P(X l An) = P(X n An) / P(An) is undefined with zero in the denominator and therefore this situation cannot be analysed as you are attempting.

What you are doing is trying to make a leap between objective probability ( or frequentist probability which assigns precise liklihoods to the various outcomes of an activity such as throwing a dice ) and subjective probability which is synonymuos with "degree of belief".

Incidentally, with 3 binary activities such as throwing a coin, the possible outcomes are :

BBB, BWW, BBW, WWW.

The probabilities of these are :

BBB and WWW - 0.125

BWW and BWW - 0.375

not 0.25 each as you persist in stating. This is schoolboy maths and suggests to me that you are not especially rigorous when dealing with mathematical probability .

Regards

Grimesy
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19-03-2013, 06:49 AM
RE: Probability
(19-03-2013 05:27 AM)Heywood Jahblome Wrote:  
(19-03-2013 05:14 AM)TheBeardedDude Wrote:  Probabilities don't accumulate.

This isn't accumulation but rather increase or decrease based on new information.
Probabilities don't change, only observations.

“Science is simply common sense at its best, that is, rigidly accurate in observation, and merciless to fallacy in logic.”
—Thomas Henry Huxley
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