Probability



11032013, 07:22 AM




RE: Probability
(11032013 02:27 AM)Heywood Jahblome 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.(11032013 02:22 AM)Aspchizo Wrote: Can you demonstrate that? or are you just going to assert your right? 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? 

11032013, 10:35 AM




RE: Probability
(11032013 06:26 AM)Kreuzfel Wrote: Starcrash, it's because of the nomemory 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 11/38=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). My mistake. I didn't notice the difference between "00" and "0". Every time I read it in my head it came out as "zero". My girlfriend is mad at me. Perhaps I shouldn't have tried cooking a stick in her nonstick pan. 

11032013, 10:47 AM




RE: Probability
What you're describing here, BlowMe, is the difference between perception and reality.
You're saying "the probability of all white marbles is increasing" but what you SHOULD be saying is "the person drawing the marbles will think, or PERCEIVE, that it is more likely to be all white marbles". Are the contents of your barrel of marbles changing after each marble is drawn (I don't mean that there is one less marble, but rather, that someone is adding or subtracting random marbles completely separately from the drawn marble)? I don't think that was your intent; I'm assuming you are positing a barrel of marbles of unknown quantity and color, but once we have said barrel, the contents remain fixed, unchanged, except for the fact that we're drawing marbles out for our experiment. Given that assumption, then before we begin drawing any marbles, we can safely state that whatever is in the barrel, even though it's unknown, it's a stable, static quantity that won't change during our experiment (other than the changes made by drawing the marbles from the barrel). So here is what's happening, including reality and including your perceptions (misperceptions): BlowMe, that's what you have been saying all throughout this thread, that YOU PERCEIVE the probability going up but you're wrong  it's going down. Hopefully I've illustrated this point well enough that you will now see the error you've made, mistaking your perception for the actual probability. I would have agreed with your initial post if you had written it like this: "What happens if you reach into the bin and pull out a white marble? You get information. You get information about the unknown composition of the bin. You know that the bin contained at least one white marble. It could contain marbles of other colors, or all the marbles that were/are in the bin could be white. You reach into the bin an pull out another white marble. You have more information about the initial composition of the bin....it had at least 2 white marbles and it seems to you that it is more likely that all marbles in the bin are white. In fact the more white marbles you draw without ever finding a non white marble, the more likely it seems to you that all marbles in the bin are white. " (those are your words from your initial post, with my edits). "Whores perform the same function as priests, but far more thoroughly."  Robert A. Heinlein 

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12032013, 12:45 AM




RE: Probability
(11032013 03:23 AM)Jakel Wrote: There are only four possible outcomes yes. But the possiblity for the combinations is not the same. Ah, Now I see how you are arriving at 1/8. As far as I am concerned WBW and WWB are the same combination but I am not going to quibble about it. It doesn't change the fact that drawing a white marble without ever drawing a black one increases the chances that all the marbles are white. 

12032013, 12:53 AM




RE: Probability
(11032013 10:47 AM)Aseptic Skeptic Wrote: What you're describing here, BlowMe, is the difference between perception and reality. The reality is you don't know the composition of the bin until you draw all the marbles. Any statements you make about the composition are going to be probabilistic ones. Suppose you and I observe a man begin to draw marbles one at a time out of a bin. We obervse him draw 17 white marbles in a row and not draw a marble of any other color. I then turn and say to you, "I'll bet you a cnote that all the marbles in the bin are white" Would you make an even money bet? 

12032013, 01:02 AM




RE: Probability
(12032013 12:45 AM)Heywood Jahblome Wrote: It doesn't change the fact that drawing a white marble without ever drawing a black one increases the chances that all the marbles are white.Unless this bin has some undisclosed property about it, where the contents are dynamically changing throughout the process, drawing marbles isn't going to change the "chances" that all of the marbles are white. They either are, or are not. Your knowledge of the contents doesn't change the probability of drawing a certain colour. The only difference is that you can't ascertain the probabilities without knowledge of its contents. If you have a bin full of white marbles, and you know that its full of white marbles, you will draw a white marble every time. If you have a bin full of white marbles, and don't know that its full of white marbles, you will draw a white marble every time. 

12032013, 01:03 AM




RE: Probability
(12032013 12:45 AM)Heywood Jahblome Wrote:That is simply not correct in this senario.(11032013 03:23 AM)Jakel Wrote: There are only four possible outcomes yes. But the possiblity for the combinations is not the same. If you roll a die 3 times and get 6 6 6, you would not (I hope....) argue that the chance of getting a 6 in the next roll is larger than 1/6. 

12032013, 01:04 AM




RE: Probability
(11032013 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. 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. 

12032013, 01:09 AM




RE: Probability
(12032013 01:03 AM)Jakel Wrote:(12032013 12:45 AM)Heywood Jahblome Wrote: Ah, Now I see how you are arriving at 1/8. As far as I am concerned WBW and WWB are the same combination but I am not going to quibble about it. It doesn't change the fact that drawing a white marble without ever drawing a black one increases the chances that all the marbles are white.That is simply not correct in this senario. Your die example is flawed because you(presumably) know that the die is properly balanced and each side is labeled with different number that spans the counting numbers 1 thru 6. You in essence know the composition of the die. If you never examined the die and all you could ever see is the result side, then the more times a 6 comes up without any other number other than 6 coming up, the more likely that each and every side of the die is labeled 6. 

12032013, 01:28 AM




RE: Probability
(12032013 01:02 AM)WeAreTheCosmos Wrote: Unless this bin has some undisclosed property about it, where the contents are dynamically changing throughout the process, drawing marbles isn't going to change the "chances" that all of the marbles are white. They either are, or are not. Your knowledge of the contents doesn't change the probability of drawing a certain colour. The only difference is that you can't ascertain the probabilities without knowledge of its contents. You are misunderstanding "probability" and "chances". Probability statements are based on the limited knowledge you have about a system and not complete knowledge of the system. If we had complete knowledge we would have no need for probability theory. 

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