Probability
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10-03-2013, 09:25 PM
RE: Probability
(10-03-2013 03:17 PM)fstratzero Wrote:  

I'm a bit of a Sam fan.

I think he did pretty well re epistemology/ontology/subjective/ objective..... in 5 minutes.

Believe he has some Buddhist leanings............... Consider
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10-03-2013, 09:51 PM
RE: Probability
(10-03-2013 09:25 PM)Mr Woof Wrote:  I'm a bit of a Sam fan.

I think he did pretty well re epistemology/ontology/subjective/ objective..... in 5 minutes.

Believe he has some Buddhist leanings............... Consider

He has gone on retreats where he claims to have spent up to eighteen hours a day meditating (Not strait I'm assuming). I do believe he has spoken to multiple Buddhists about meditation, he appears to think very positively of them. I think he speaks about these in one of his videos.

Perhaps this one...



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11-03-2013, 12:23 AM
RE: Probability
(10-03-2013 03:36 PM)Jakel Wrote:  no. 3 marbles means 1/8 chance of all whites, if the marbles in the bin are black or white with 50/50 chance?

Jakel, I came up with the idea of using three marbles and thier possible combination as a means of proving my point while I was in church. I didn't have a lot of time after church to make that post before other commitments kicked in so I wrote it in haste and could have made an error. Still I don't see how you are coming up with 1/8th?

Are you considering the following combinations to be different?

BBW BWB WBB

I am treating these as all the same combination. I still only see 4 possible combinations for 3 marbles and if any one is just as likely as the rest, then each one has an initial probability of .25 to be the true combination.

Vosur, Anjele, Hanoff.....have you learned nothing in my absence?
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11-03-2013, 01:58 AM
RE: Probability
(10-03-2013 06:26 PM)kim Wrote:  If no one knows the amount or color of marbles in the bin then "the more likely it becomes" is a speculative statement connecting evidence with a declarative statement.

It is assumed that the amount of marbles in the bin is greater than 0. The example I provided works with an positive amount of marbles. "the more likely it becomes" is indeed a factual statement and not a speculative one as you suggest.

Vosur, Anjele, Hanoff.....have you learned nothing in my absence?
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11-03-2013, 02:22 AM
RE: Probability
(11-03-2013 01:58 AM)Heywood Jahblome Wrote:  
(10-03-2013 06:26 PM)kim Wrote:  If no one knows the amount or color of marbles in the bin then "the more likely it becomes" is a speculative statement connecting evidence with a declarative statement.

It is assumed that the amount of marbles in the bin is greater than 0. The example I provided works with an positive amount of marbles. "the more likely it becomes" is indeed a factual statement and not a speculative one as you suggest.

Can you demonstrate that? or are you just going to assert your right?

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11-03-2013, 02:27 AM (This post was last modified: 11-03-2013 02:33 AM by Heywood Jahblome.)
RE: Probability
(11-03-2013 02:22 AM)Aspchizo Wrote:  Can you demonstrate that? or are you just going to assert your right?

The reason the claim is true is because as you draw out white marbles, there are less ways the bin can contain black ones(let black mean any other color here). For instance suppose the bin has only 3 marbles. Let W stand for white marble and B stand for a black one. There are only 4 possible combinations of marbles.

  1. BBB
  2. BBW
  3. BWW
  4. WWW
If each combination is equally likely, then each has a .25 probability of being the true combination. Please note that before starting the draws the probability of the bin containing just white marbles is .25. What happens if on the first draw we draw white? Well a white draw eliminates combination 1. With only three remaining possible combinations the probability that the bin only contains white marbles rises to .33. Drawing a second white marble eliminates combination 2 and the probability of the bin only containing white marbles rises to .5. Of course if you draw a third marble and it is white, then the probability the bin only contained white marbles is of course 1.

I hope this example shows that the Probabiltiy of X(all the marbles in the bin are white) is an increasing function of An(n white draws without ever observing a black one). This demonstration is in agreement with the mathematical proof I provided earlier.

Vosur, Anjele, Hanoff.....have you learned nothing in my absence?
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11-03-2013, 03:23 AM (This post was last modified: 11-03-2013 11:18 AM by Jakel.)
RE: Probability
(11-03-2013 12:23 AM)Heywood Jahblome Wrote:  
(10-03-2013 03:36 PM)Jakel Wrote:  no. 3 marbles means 1/8 chance of all whites, if the marbles in the bin are black or white with 50/50 chance?

Jakel, I came up with the idea of using three marbles and thier possible combination as a means of proving my point while I was in church. I didn't have a lot of time after church to make that post before other commitments kicked in so I wrote it in haste and could have made an error. Still I don't see how you are coming up with 1/8th?

Are you considering the following combinations to be different?

BBW BWB WBB

I am treating these as all the same combination. I still only see 4 possible combinations for 3 marbles and if any one is just as likely as the rest, then each one has an initial probability of .25 to be the true combination.
There are only four possible outcomes yes. But the possiblity for the combinations is not the same.
There are 2^3=8 combinations yes:

WWW WWB WBB WBW BWW BWB BBB BBW

If each marbles drawn have the same possibility of being white or black, and the draws are independent
the probability of WWW is 1/8.

Another way to see it, is that if the probability of drawing white/black is 50/50 and independent, then the probability for WWW=0.5*0.5*0.5=0.125=1/8.

EDIT: I changed "combinations" to "outcomes" in the start
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11-03-2013, 04:19 AM
Rainbow RE: Probability
I agree with Haywood Jablome that in the fair roulette example, the one with 00,0,1,...,36 slots has 1/38 probability of 00, so, if after one million plays the 00 didn't show, the roulette has a much higher probability of being single 0. The example of marbles is less clear bacause we have an infinite amount of marbles and colors. If we can change it a bit, and know the initial conditions, then we can say something about probability. In this case we could say that there are only two possibilities for a magic machine (hidden inside a box) that will instantly generate a marble (and can do it infinite times): one will always generate a white marble, the other will generate a white marble with 50% chance and a black one with 50% chance. In this case, if after a lots of extractions all the marbles are white, the probability of having the "all white" machine is much higher.

I do not see particular flaws in the reasoning of Jablome, maybe the only problem is that he picked a foggy example (at least for me). Smartass

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11-03-2013, 05:31 AM
RE: Probability
(11-03-2013 04:19 AM)Kreuzfel Wrote:  I agree with Haywood Jablome that in the fair roulette example, the one with 00,0,1,...,36 slots has 1/38 probability of 00, so, if after one million plays the 00 didn't show, the roulette has a much higher probability of being single 0.

I didn't read this before, but this is the textbook example of the Gambler's Fallacy. A roulette wheel doesn't have a memory, so no single number ever becomes more likely simply because it hasn't come up in a long time. I don't have a problem with the marble-drawing example (although I agree that it's murky) but if this one was suggested, it's blatantly wrong.

My girlfriend is mad at me. Perhaps I shouldn't have tried cooking a stick in her non-stick pan.
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11-03-2013, 06:26 AM
RE: Probability
Starcrash, it's because of the no-memory thing that the 00 will have always a 1/38 probability of showing up regardless of what showed up before (in particular it does not become more likely to appear if it didn't appear before). For this very reason, the probability of not showing up is 1-1/38=37/38, the probability of not showing up for 2 times in a row is (37/38)^2 and so on... So the probability of not showing up after one million times is practically zero (1.34*10^(-11582))... So, if after a lot of plays it doesn't show up there is an high chance that we are dealing with a single 0 roulette (assuming the roulette is fair, of course).

We walk by faith, not by sight. Angel
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