Probability



20032013, 11:11 AM




RE: Probability
(20032013 07:43 AM)pgrimes15 Wrote:(20032013 12:47 AM)Heywood Jahblome Wrote: Grimesy, you are in error. An is always greater than 0 by definition. Think about it this way, An is n white marble draws in a row. P(An) is the probability of n white marbles in a row. As long as it is logically possible to draw a white P(An) is greater than 0 for any n. Is the probability of drawing 5 white marbles in a row greater than 0? Or 10 white marbles in a row? Or a billion? Yes, if the composition of the bin is unknown to you then the assumption that it is logically possible to draw another white marble is reasonable. I agree it does feel like pigeon chess. P(XAn) means the probability of X given An. Remember that An is a condition and that we talking about the probability of X only under the condition An. If a black marble is drawn the proof does not apply. Do you agree now that it was silly of you to claim that P(An) is 0 if a black marble is drawn? 

20032013, 11:20 AM




Re: Probability
The probabilities were calculated off of the observations and do not indicate what the number of colors actually is within the bucket, only the number of colors drawn.
And probabilities are our estimates of our observations and must necessarily be estimated as they always have some associated variance. Your answer of "5 or more" means infinity, and there was a finite number of colors. This is the point. Observations only indicate what we observe and there could still be some infinite number of colors in the bucket. Even when there isn't, we can't assert that based on our observations. Now, let's say we make a technological breakthrough that changes the frequency at which we start drawing out the nonwhite colors such that our 4 colors now come out in equal proportions. Were our first observations wrong? Were the calculated probabilities wrong? Is our current method wrong? 

20032013, 11:24 AM




Re: Probability
It should also be pointed out that probabilities calculated from observations are estimates but probabilities calculated mathematically from known variations in the system are not estimates.
Ergo, knowing that a coin has 2 sides leads to a probability of 50/50 But calculating a probability off of some number of trials will give something close to 50/50 (assuming enough trials) with a variance that means this probability is an estimate. 

20032013, 12:01 PM




RE: Probability
(20032013 11:20 AM)TheBeardedDude Wrote: The probabilities were calculated off of the observations and do not indicate what the number of colors actually is within the bucket, only the number of colors drawn. 5 or more does not mean infinity. It means 5(which is finite) or some number(all numbers are finite) greater than 5. To answer your questions, our first observations where not wrong(unless the observer is color blind or something). Were are estimates wrong? Sure but the method is sound. Just because it appeared likely there were only 4 colors doesn't preclude the chance of an outlier. I never claimed there could not be outliers. 

20032013, 12:09 PM




RE: Probability
(20032013 11:24 AM)TheBeardedDude Wrote: It should also be pointed out that probabilities calculated from observations are estimates but probabilities calculated mathematically from known variations in the system are not estimates.. Only if it is assumed that the results of a flip are random and the coin is true. Incidentally there was a study done which claims it is more likely a coin will land on the same side it started. 

20032013, 12:59 PM




RE: Probability
Really? We're still here?
At some point, we all have to realize that BlowJob is not the least bit interested in learning about probability. He's trolling, stirring up trouble, and laughing at how much energy everyone is wasting trying to educate his sorry ass. If he cared at all, he would have clued in by now, and surely he did, but that's not why he's keeping this thread alive, arguing in circles, ignoring everyone's rebuttals. "Whores perform the same function as priests, but far more thoroughly."  Robert A. Heinlein 

20032013, 01:07 PM




Re: Probability
This does appear to be nothing more than a circlejerk. Especially when examples are given for coin flips and the qualifier of "If it is a true coin" comes out.
Go grab a stats book. 

20032013, 01:34 PM




RE: Probability
(20032013 12:59 PM)Aseptic Skeptic Wrote: Really? We're still here? I forgive you for spreading these lies about me. 

20032013, 01:38 PM




RE: Probability
(20032013 01:07 PM)TheBeardedDude Wrote: Go grab a stats book. That's good advice you would do well to follow. 

20032013, 01:55 PM




Re: Probability
I have a few. Had to have them for Intro to stats, multivariate statistics, and ANOVA and experimental design.


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