Probability
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15-03-2013, 10:01 AM
RE: Probability
At sample size 720, number of colors = 3.67, variability = 0.43

Best guess is still 4, and that is still wrong.


The point is this. For examples like the coin, we already know how many possibilities there are, so we can mathematically show that the actual probability of any given sample is 0.5. But in nature, we don't know what the true probabilities are. We would have to actually flip the coin to see what we could get.


If I flip it one trillion times, I will get something approaching 50/50, but my odds of exactly half a trillion heads and half a trillion tails, is the same as my odds of getting 1 trillion heads or 1 trillion tails.

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15-03-2013, 10:22 AM
RE: Probability
At sample size 860, number of colors = 3.78, variability = 0.45

Best guess is still 4, and that is still wrong.

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15-03-2013, 10:41 AM
RE: Probability
4 is always the answer. Silly. Big Grin

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15-03-2013, 10:52 AM
RE: Probability
I am ending it here at sample size 1020, number of colors = 3.89, variability = 0.48

Best guess is still 4, and that is still wrong.

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15-03-2013, 01:25 PM
RE: Probability
(15-03-2013 10:01 AM)TheBeardedDude Wrote:  If I flip it one trillion times, I will get something approaching 50/50, but my odds of exactly half a trillion heads and half a trillion tails, is the same as my odds of getting 1 trillion heads or 1 trillion tails.

Ummm, no. Not even close. Consider

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15-03-2013, 01:38 PM
RE: Probability
(15-03-2013 01:25 PM)Chas Wrote:  
(15-03-2013 10:01 AM)TheBeardedDude Wrote:  If I flip it one trillion times, I will get something approaching 50/50, but my odds of exactly half a trillion heads and half a trillion tails, is the same as my odds of getting 1 trillion heads or 1 trillion tails.

Ummm, no. Not even close. Consider
The odds of getting a single exact number (assuming sample size is infinity) is the same as getting a single exact number of any other.

So, the odds of getting one number in the powerball, is the same as the odds of getting any other. (once again, we are assuming that the balls are replaced once drawn).

That is because with each coin flip, the odds reset back to 50/50. They don't accumulate.

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15-03-2013, 01:46 PM
RE: Probability
(15-03-2013 01:38 PM)TheBeardedDude Wrote:  
(15-03-2013 01:25 PM)Chas Wrote:  Ummm, no. Not even close. Consider
The odds of getting a single exact number (assuming sample size is infinity) is the same as getting a single exact number of any other.

So, the odds of getting one number in the powerball, is the same as the odds of getting any other. (once again, we are assuming that the balls are replaced once drawn).

That is because with each coin flip, the odds reset back to 50/50. They don't accumulate.

No. There is only 1 way, each, to get a trillion heads or tails.

There are a many, many ways to get half heads and half tails.

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15-03-2013, 01:53 PM
RE: Probability
(15-03-2013 01:46 PM)Chas Wrote:  
(15-03-2013 01:38 PM)TheBeardedDude Wrote:  The odds of getting a single exact number (assuming sample size is infinity) is the same as getting a single exact number of any other.

So, the odds of getting one number in the powerball, is the same as the odds of getting any other. (once again, we are assuming that the balls are replaced once drawn).

That is because with each coin flip, the odds reset back to 50/50. They don't accumulate.

No. There is only 1 way, each, to get a trillion heads or tails.

There are a many, many ways to get half heads and half tails.

Okay, assuming a normal distribution, the probability of something approaching 50/50 is higher in a coin-flip scenario. I stand corrected.

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15-03-2013, 02:40 PM
RE: Probability
Hey, BlowMe, why haven't you figured this out yet.

It's not that your math is so wrong, or your examples so wrong, it's that you have come to the very wrong conclusion that the probability is changing. It isn't. The only thing changing is the observer who is making changing guesses about the probability based on his observations.

Before drawing any marbles, if all he knows is that there are marbles in a barrel, he will have no assumptions. After drawing one white one, he can "know" that he barrel did not contain all non-white, and he "know" it had some white, but he has no idea how many white. After drawing more white marbles (and no other colors at all) he still doesn't "know" anything new, but he starts to make assumptions that the barrel probably contains mostly, or even all, white marbles. Whatever the barrel actually contains is not changing based on the assumptions, nor is it changing based on what has already been drawn (well, it has fewer marbles so it IS changing in that regard, but the original contents are not changing based on drawn marbles).

Your example only shows how people make assumptions from observations.

But you insist that the probability is changing, getting "more likely" that the barrel is all white. The PROBABILITY is not changing; only the guessing is changing.

Why are you too dense to grasp this?

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15-03-2013, 03:31 PM
RE: Probability
(15-03-2013 02:40 PM)Aseptic Skeptic Wrote:  Hey, BlowMe, why haven't you figured this out yet.

It's not that your math is so wrong, or your examples so wrong, it's that you have come to the very wrong conclusion that the probability is changing. It isn't. The only thing changing is the observer who is making changing guesses about the probability based on his observations.

Before drawing any marbles, if all he knows is that there are marbles in a barrel, he will have no assumptions. After drawing one white one, he can "know" that he barrel did not contain all non-white, and he "know" it had some white, but he has no idea how many white. After drawing more white marbles (and no other colors at all) he still doesn't "know" anything new, but he starts to make assumptions that the barrel probably contains mostly, or even all, white marbles. Whatever the barrel actually contains is not changing based on the assumptions, nor is it changing based on what has already been drawn (well, it has fewer marbles so it IS changing in that regard, but the original contents are not changing based on drawn marbles).

Your example only shows how people make assumptions from observations.

But you insist that the probability is changing, getting "more likely" that the barrel is all white. The PROBABILITY is not changing; only the guessing is changing.

Why are you too dense to grasp this?

First, I forgive you for calling me dense.

Second, you are making the same error that Chas made. You are conflating probability with reality. Probability is not reality. Probability is a measure or estimation of how likely it is that some event will occur( or has occurred if we are unable to observe it). This estimation or measure can change with the introduction of new information.
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