Probability
Post Reply
 
Thread Rating:
  • 3 Votes - 3 Average
  • 1
  • 2
  • 3
  • 4
  • 5
12-03-2013, 07:30 AM (This post was last modified: 12-03-2013 07:35 AM by Vosur.)
RE: Probability
(12-03-2013 01:04 AM)Heywood Jahblome Wrote:  If anyone wants to continue, show a fatal flaw in the last example I provided or the mathematical proof I provided.
It has already been done several times. If you still don't understand it, tough luck.

[Image: 7oDSbD4.gif]
Find all posts by this user
Like Post Quote this message in a reply
12-03-2013, 07:53 AM
RE: Probability
(12-03-2013 01:04 AM)Heywood Jahblome Wrote:  
(11-03-2013 07:22 AM)TheBeardedDude Wrote:  Assuming an infinite number of black and white marbles, you would be more or less correct statistically in saying that the probability of attaining anyone of the 4 possibilities in the above scenario is 0.25. If, however, the number of marbles is finite, then the probabilities change each time you draw a marble.

Start off of with small numbers first. If you only have 4 marbles (2 black and 2 white), you have a 50/50 chance of your first draw of getting a white marble, but after that draw, the probabilities change.

Let's say you had those 4 marbles
Before draw 1, odds of a white marble = 50%
Draw one = White

Before draw 2, odds of a white marble = 33%
Draw three = Black

Before draw 3, odds of a white marble = 50%
Draw three = white

Before draw 4, odds of a white marble = 0%
Draw four = Black


Let me ask you one simple question. Are statistics and probabilities descriptive, predictive, or both?

The problem we are trying to solve isn't what is the probability of drawing a white marble or a black one. We are trying to answer the question, does observing just white marbles being drawn(without ever observing a blackone) increase the probability that all the marbles are white?

I think that the mathematical proof I provided, along with the example I provided, proves conclusively that the answer to the question is yes.

I'm not sure why we are still debating this....its as silly as debating if evolution actually happens. If anyone wants to continue, show a fatal flaw in the last example I provided or the mathematical proof I provided.
You didn't answer my question. It is essential if you want to know what is wrong with your conclusion.

“Science is simply common sense at its best, that is, rigidly accurate in observation, and merciless to fallacy in logic.”
—Thomas Henry Huxley
Find all posts by this user
Like Post Quote this message in a reply
12-03-2013, 10:05 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)?
P(X|An) means the probability of X given that An has already occurred.
Find all posts by this user
Like Post Quote this message in a reply
12-03-2013, 10:22 AM
RE: Probability
(12-03-2013 10:05 AM)Heywood Jahblome Wrote:  
(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)?
P(X|An) means the probability of X given that An has already occurred.
Yes. And X is difined as the probability of all the marbles being white. Your notation does not make sense. If you can't see this, you are not in a position to discuss this subject. How did you obtain this so-called "proof"?
Find all posts by this user
Like Post Quote this message in a reply
12-03-2013, 10:24 AM
RE: Probability
(12-03-2013 07:53 AM)TheBeardedDude Wrote:  
(12-03-2013 01:04 AM)Heywood Jahblome Wrote:  The problem we are trying to solve isn't what is the probability of drawing a white marble or a black one. We are trying to answer the question, does observing just white marbles being drawn(without ever observing a blackone) increase the probability that all the marbles are white?

I think that the mathematical proof I provided, along with the example I provided, proves conclusively that the answer to the question is yes.

I'm not sure why we are still debating this....its as silly as debating if evolution actually happens. If anyone wants to continue, show a fatal flaw in the last example I provided or the mathematical proof I provided.
You didn't answer my question. It is essential if you want to know what is wrong with your conclusion.
Statistics and probabilities are both descriptive and predictive.....I don't see how answering your question invalidates my conclusion.
Find all posts by this user
Like Post Quote this message in a reply
12-03-2013, 10:30 AM
RE: Probability
(12-03-2013 10:22 AM)Jakel Wrote:  
(12-03-2013 10:05 AM)Heywood Jahblome Wrote:  P(X|An) means the probability of X given that An has already occurred.
Yes. And X is difined as the probability of all the marbles being white. Your notation does not make sense. If you can't see this, you are not in a position to discuss this subject. How did you obtain this so-called "proof"?
The probability that all marbles are white given that n draws has occurred (with each being white), is a perfectly sensical statement.
Find all posts by this user
Like Post Quote this message in a reply
12-03-2013, 10:52 AM (This post was last modified: 12-03-2013 10:56 AM by Heywood Jahblome.)
RE: Probability
(12-03-2013 10:22 AM)Jakel Wrote:  
(12-03-2013 10:05 AM)Heywood Jahblome Wrote:  P(X|An) means the probability of X given that An has already occurred.
Yes. And X is difined as the probability of all the marbles being white. Your notation does not make sense. If you can't see this, you are not in a position to discuss this subject. How did you obtain this so-called "proof"?
AHH HAH!

I see it now. Yes I made the error you are pointing out. Thank you so much! Here is the corrected proof.

Let X = there are no black marbles(black means any other color here).
Let An = n draws of white marbles without ever drawing a black 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.
Find all posts by this user
Like Post Quote this message in a reply
12-03-2013, 11:12 AM
RE: Probability
(12-03-2013 10:52 AM)Heywood Jahblome Wrote:  
(12-03-2013 10:22 AM)Jakel Wrote:  Yes. And X is difined as the probability of all the marbles being white. Your notation does not make sense. If you can't see this, you are not in a position to discuss this subject. How did you obtain this so-called "proof"?
AHH HAH!

I see it now. Yes I made the error you are pointing out. Thank you so much! Here is the corrected proof.

Let X = there are no black marbles(black means any other color here).
Let An = n draws of white marbles without ever drawing a black 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.
Now we are going somewhere. Next questions
-Just to make sure. By "A & B" you mean the intersection of A and B right?
-How do you get P(X | An+1 & An)=P(X | An+1)?
Find all posts by this user
Like Post Quote this message in a reply
12-03-2013, 12:50 PM
RE: Probability
I wouldn't be willing to state without any doubt that all the marbles in the bin are white when I know no such thing.

The future is unknown and unknowable and I personally don't think I would care for it to be otherwise. I guess some people think that "wish fulfillment" or whatever you call it, is a good thing but I just see it as what might be a false promise wrapped in some conclusion, hastily jumped to - maybe out of desperation or fear or something - I don't really know. I do not gamble - don't care about it at all - so no, I wouldn't wager money or anything else that all the marbles in the bin are white. I think I'm just gonna guess that not everyone got that "gambling can be addictive" memo.

So, all this entire jerk-off thread tells anyone is that JahwehBlow is ready and willing to jump to a conclusion that the average skeptic just isn't. Good luck with your leap of faith; I don't have that. Drinking Beverage

A new type of thinking is essential if mankind is to survive and move to higher levels. ~ Albert Einstein
Find all posts by this user
Like Post Quote this message in a reply
12-03-2013, 01:17 PM
RE: Probability
(12-03-2013 10:24 AM)Heywood Jahblome Wrote:  
(12-03-2013 07:53 AM)TheBeardedDude Wrote:  You didn't answer my question. It is essential if you want to know what is wrong with your conclusion.
Statistics and probabilities are both descriptive and predictive.....I don't see how answering your question invalidates my conclusion.
Statistics and probabilities are descriptive only. They describe observations and describe data. They are not predictors of anything and can only be used to interpret past results. If someone makes an assumption about the future (or even the present), they may use the past (statistics) to say something about the probability that the past will repeat itself (statistics), but it does not actually predict what will happen.

So, someone drawing marbles from a bucket might continuously draw white marbles, but their statistical calculations only describe their observation. It makes no prediction about the contents of the bucket. This is also why the probability of white marbles would approach 1 with each draw of a white marble, but not reach 1 (or 100%).

You are making the false assumption of using statistics to predict something, and you are just flat-out wrong.

“Science is simply common sense at its best, that is, rigidly accurate in observation, and merciless to fallacy in logic.”
—Thomas Henry Huxley
Find all posts by this user
Like Post Quote this message in a reply
[+] 2 users Like TheBeardedDude's post
Post Reply
Forum Jump: