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Post by rational on Dec 2, 2015 14:24:47 GMT -5
In the case of the dice, you are wrong. You are attempting to single out one roll. So yes, one roll would have a 1 in 6 chance of rolling a 6. This is correct.Actually you would have a 166.6666... in 1,000 of rolling a 6, or a 1 in 6 chance, or you would expect a 6 16.666...% of the time.Yes, but there is a possibility that the first 166.66... rolls could be a 6. The failures (non-6 rolls) are not a requirement and do not influence nor are in any way part of how each die is rolled. The probability of rolling 166 '6's is slim. The die has no memory. No matter how many rolls you are making each one is independent and separate from all previous and subsequent rolls. No. If the DNA was not passed on it did not exert any influence on future generations. Can you put forth a case where a species that has gone extinct was able to influence future generations?c possibility The DNA that WAS passed on. So his statement is true.[/quote]
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Post by jondough on Dec 2, 2015 16:03:17 GMT -5
In the case of the dice, you are wrong. You are attempting to single out one roll. So yes, one roll would have a 1 in 6 chance of rolling a 6. This is correct.Actually you would have a 166.6666... in 1,000 of rolling a 6, or a 1 in 6 chance, or you would expect a 6 16.666...% of the time. Yes. Yes, but there is a possibility that the first 166.66... rolls could be a 6. The failures (non-6 rolls) are not a requirement and do not influence nor are in any way part of how each die is rolled. The probability of rolling 166 '6's is slim. The die has no memory. No matter how many rolls you are making each one is independent and separate from all previous and subsequent rolls. No. If the DNA was not passed on it did not exert any influence on future generations. Can you put forth a case where a species that has gone extinct was able to influence future generations?c possibility The DNA that WAS passed on. So his statement is true. [/quote] In order to roll 166 6's, you must roll 1000 times. You WILL NOT roll 166 6's by only rolling 166 times. The law of probability will not allow it. Therefore, the other 834 "sacrificial" rolls are necessary in order to for the result of 166 6's.
Here is his statement again: "According to evolution everything that is owes its existence to everything that was"
So he isn't claiming that the DNA being passed on is necessarily for being responsible for the existence of everything that is. You are claiming that the "sacrificial" specimens that died out were not necessary. Typical to the "sacrificial" rolls as explained above, they were for the same reasons. For this reason, his statement is true.
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Post by matisse on Dec 2, 2015 16:37:26 GMT -5
This is correct.Actually you would have a 166.6666... in 1,000 of rolling a 6, or a 1 in 6 chance, or you would expect a 6 16.666...% of the time. Yes. Yes, but there is a possibility that the first 166.66... rolls could be a 6. The failures (non-6 rolls) are not a requirement and do not influence nor are in any way part of how each die is rolled. The probability of rolling 166 '6's is slim. The die has no memory. No matter how many rolls you are making each one is independent and separate from all previous and subsequent rolls. No. If the DNA was not passed on it did not exert any influence on future generations. Can you put forth a case where a species that has gone extinct was able to influence future generations?c possibility The DNA that WAS passed on. So his statement is true. In order to roll 166 6's, you must roll 1000 times. You WILL NOT roll 166 6's by only rolling 166 times. The law of probability will not allow it. Therefore, the other 834 "sacrificial" rolls are necessary in order to for the result of 166 6's.
Here is his statement again: "According to evolution everything that is owes its existence to everything that was"
So he isn't claiming that the DNA being passed on is necessarily for being responsible for the existence of everything that is. You are claiming that the "sacrificial" specimens that died out were not necessary. Typical to the "sacrificial" rolls as explained above, they were for the same reasons. For this reason, his statement is true.
[/quote] There is a ridiculously small, but finite probability that you will roll 1000 times and get a 6 every time. There is a substantially greater probability (though still ridiculously small) that you will roll 1000 times and not get any 6's.
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Post by SharonArnold on Dec 2, 2015 16:43:14 GMT -5
So in evolution, probability has been a huge necessary factor. The unsuccessful (rolls) or DNA that wasn't passed on was necessary in order to for the successful results. No. If the DNA was not passed on it did not exert any influence on future generations. Can you put forth a case where a species that has gone extinct was able to influence future generations?c possibility The DNA that WAS passed on. So his statement is true. I don’t particularly like the dice argument, though I do not think you can completely discount probabilities where understanding evolution is concerned. However, I find the assertion “ If the DNA was not passed on it did not exert any influence on future generations” is spoken like a true materialist. Do you suppose that your contributions to evolution to life on this planet is limited to what DNA you have passed on? For example, what about your participation even on this Bulletin Board? Do you suppose that no future generations are becoming “Rat-proofed” because of your contributions here? Or to re-frame the question in slightly more prosaic terms. Suppose there was a species (or individual within a species) that was slower than most. It did not get a chance to pass on its DNA before being eaten by a predator. But, because it was there for that predator, another species/individual within a species did survive and did have the chance to pass on its DNA? Did the first one really have zero contribution to the unfoldment of life of this planet? The Butterfly Effect seems kind of right to me. But then, I am not into materialism. Or naïve realism.
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Post by jondough on Dec 2, 2015 16:54:57 GMT -5
In order to roll 166 6's, you must roll 1000 times. You WILL NOT roll 166 6's by only rolling 166 times. The law of probability will not allow it. Therefore, the other 834 "sacrificial" rolls are necessary in order to for the result of 166 6's.
Here is his statement again: "According to evolution everything that is owes its existence to everything that was"
So he isn't claiming that the DNA being passed on is necessarily for being responsible for the existence of everything that is. You are claiming that the "sacrificial" specimens that died out were not necessary. Typical to the "sacrificial" rolls as explained above, they were for the same reasons. For this reason, his statement is true.
There is a ridiculously small, but finite probability that you will roll 1000 times and get a 6 every time. There is a substantially greater probability (though still ridiculously small) that you will roll 1000 times and not get any 6's.[/quote] No. The rules of probability will ALWAYS rule. Always always. The more times you roll, the more exact the rule will become. In other words, if you only roll the dice 6 times, there is a good chance that you will not roll a 6 16.66% of the time. But if you roll a million times, you WILL roll a 6 16.66% of the time. Probability WILL always rule in the long run. Non fail.
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Post by jondough on Dec 2, 2015 17:05:19 GMT -5
No. If the DNA was not passed on it did not exert any influence on future generations. Can you put forth a case where a species that has gone extinct was able to influence future generations?c possibility The DNA that WAS passed on. So his statement is true. I don’t particularly like the dice argument, though I do not think you can completely discount probabilities where understanding evolution is concerned. However, I find the assertion “ If the DNA was not passed on it did not exert any influence on future generations” is spoken like a true materialist. Do you suppose that your contributions to evolution to life on this planet is limited to what DNA you have passed on? For example, what about your participation even on this Bulletin Board? Do you suppose that no future generations are becoming “Rat-proofed” because of your contributions here? Or to re-frame the question in slightly more prosaic terms. Suppose there was a species (or individual within a species) that was slower than most. It did not get a chance to pass on its DNA before being eaten by a predator. But, because it was there for that predator, another species/individual within a species did survive and did have the chance to pass on its DNA? Did the first one really have zero contribution to the unfoldment of life of this planet? The Butterfly Effect seems kind of right to me. But then, I am not into materialism. Or naïve realism. This makes the same point I was feebly trying to make, that is, passing on the DNA is not the only thing that affects the future. Your example is a good one. Or how about the species that died and didn't pass on the DNA, but decayed, fed the plants that the strong species ate. Remember Mufasa's Cirle of Life?
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Post by rational on Dec 2, 2015 19:05:39 GMT -5
In order to roll 166 6's, you must roll 1000 times. Nope. You migt have to roll the die 1198 times. Or you might get to 166 by only rolling 500 times. There is the possibility that you could roll 1000 times and not get a single 6.Well, this is simply wrong. The probability only serves to predict an outcome, not determine the outcome. While the probability of getting 1666 '6's in a row is small, as they say, it is a small but non-zero probability.You keep saying this but it is completely wrong. The only thing that is required to get 166 '6's is that the die rolls to a '6' 166 times. Consider this: You sit at the table and prepare to roll the die. The odds it will be a '6' are 1 in 6. It is a six. You pick up the die and prepare to roll it again. The odds it will be a '6' are 1 in 6. It is a six. You pick up the die and wonder what the odds are of getting another '6'. For this roll the odds are, of course, 1 in 6. It is a six. We have all sat and rolled a die and got three of something in a row. It is possible to get 3 '6's in a row. If it is possible to do it once, it is possible to do it again. And again to get 9 '6's in a row. And so on. No matter what the past results have been, for every roll the odds stay the same. I see what you are saying. But the quote was about the evolution of organisms and that does involve the passing of genetic material. Evolution is accomplished by genetic changes in a species being passed to their offspring. If it is an advantageous change the probability of there being a greater number of individuals producing even more individuals with the advantageous DNA. However, if the species becomes extinct there is no passing of the DNA. No individuals benefit from the dead end species. They were not. Whatever their DNA was or what ever changes they experienced were not passed along and therefore were of no use to the species that did survive.Except for your premise that somehow the failures were somehow required. As an example: During embryonic development the DNA of a man is modified (inaccurate chromosome copy or a modification caused by radiation) and he develops complete immunity to all known bacteria and viruses. Unfortunately the same change also made him sterile. A promising evolutionary change that resulted in a dead end. Nothing that is owes its existence to this individual.
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Post by jondough on Dec 2, 2015 19:18:41 GMT -5
You are wrong about the law of probability. Enough experiments have been done on this. I've been witness to one. The law of probability always rules. You can attempt to keep isolating it to one and talk about the one by itself, but when you do that 1000 times, you no longer have just one, you have a 1000. The law of probability would then be applicable to 1000, not just one like you keep trying to do.
Surely you know why the casinos in Vegas make money year end, year out - so long as they have enough volume? Thats right. Because the laws of probability always work.
This horse has been beat enough.
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Post by rational on Dec 2, 2015 19:23:02 GMT -5
I don’t particularly like the dice argument, though I do not think you can completely discount probabilities where understanding evolution is concerned. Nor do I but you need to use statistics correctly. Or perhaps a biologist. Evolution involves the modification and passing of genetic material. It is actually based on real matter. By definition, yes. As far as evolution of organisms, it is accomplished by passing changes from one generation to the next by genetic material. No, I don't think anything accomplished on this message board will be passed via genetic material to my offspring. The non-reproductive individual did not contribute anything to the evolution of the species. Perhaps a quick definition of evolution from wikipedia is in order: Evolution is change in the heritable traits of biological populations over successive generations.But then it really doesn't speak to evolution. Or biological evolution.
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Post by SharonArnold on Dec 2, 2015 19:37:13 GMT -5
I don’t particularly like the dice argument, though I do not think you can completely discount probabilities where understanding evolution is concerned. Nor do I but you need to use statistics correctly. Or perhaps a biologist. Evolution involves the modification and passing of genetic material. It is actually based on real matter. By definition, yes. As far as evolution of organisms, it is accomplished by passing changes from one generation to the next by genetic material. No, I don't think anything accomplished on this message board will be passed via genetic material to my offspring. The non-reproductive individual did not contribute anything to the evolution of the species. Perhaps a quick definition of evolution from wikipedia is in order: Evolution is change in the heritable traits of biological populations over successive generations.But then it really doesn't speak to evolution. Or biological evolution. These definitions are equally correct: ev·o·lu·tion /ˌevəˈlo͞oSH(ə)n/ noun noun: evolution; plural noun: evolutions 1. the process by which different kinds of living organisms are thought to have developed and diversified from earlier forms during the history of the earth. 2. the gradual development of something, especially from a simple to a more complex form. The field of biology is not excluded from either of these. I think, on another thread, you recently suggested to Alvin that he should do some reading. I might suggest the same to you. Starting with epigenetics, and then maybe some quantum biology. (Way crazier than its application in physics.) Then maybe go stare at the night sky for a while.
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Post by rational on Dec 2, 2015 19:50:28 GMT -5
These definitions are equally correct: ev·o·lu·tion /ˌevəˈlo͞oSH(ə)n/ noun noun: evolution; plural noun: evolutions 1. the process by which different kinds of living organisms are thought to have developed and diversified from earlier forms during the history of the earth. 2. the gradual development of something, especially from a simple to a more complex form. They are correct but neither addresses the mechanism that produces the change. In the context of the discussion it was the evolution of organisms. Hard to get away from genetic material in that context. Epigenetics does not figure heavily into the modification of the genetic structure that would be transferred to successive generations. A billion years of natural selection allows, for example, bacteria to take advantage of all sorts of quantum shenanigans! In the dark? Sounds risky!
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Post by SharonArnold on Dec 2, 2015 22:18:32 GMT -5
Then maybe go stare at the night sky for a while. In the dark? Sounds risky! Life on the edge! Go for it! You might even find that a little poetry, a sense of wonder, creeps into your soul. (Yeah, yeah. I know you think you don't have one!)
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Post by ellie on Dec 3, 2015 8:18:06 GMT -5
You are wrong about the law of probability. Enough experiments have been done on this. I've been witness to one. The law of probability always rules. You can attempt to keep isolating it to one and talk about the one by itself, but when you do that 1000 times, you no longer have just one, you have a 1000. The law of probability would then be applicable to 1000, not just one like you keep trying to do. Surely you know why the casinos in Vegas make money year end, year out - so long as they have enough volume? Thats right. Because the laws of probability always work. This horse has been beat enough. Perhaps you are thinking in terms of averages rather than probability law? If you roll a dice 3 times the probability of rolling a 6 every time is 1/6 x 1/6 x 1/6. I.e (1/6)^3. If you roll your dice 166 times the probability of rolling 166 consecutive 6’s (although low) is non-zero. The probability is (1/6)^166. Dice rolls are always independent events. It does not matter if a dice has been rolled 0 times 1 time or 1000 times. Each and every roll is independent of the previous roll and the subsequent roll. The probability of any number turning up on a regular 6 sided dice throw is always 1/6. The probability is always constant.
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Post by jondough on Dec 3, 2015 9:15:30 GMT -5
Watch the video of the balls. Forget the financial stuff he's talking about. Just notice that the balls have the greatest probability (predictably) to fall in the center, then a predictable less probability of falling in the outer columns. This is a great example of probability working perfectly and predictably over the long term, and upon many tries. This is what I've been trying to communicate.
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Post by jondough on Dec 3, 2015 9:48:39 GMT -5
So my original point was (using this machine as an example) in order to get 5 balls in the outer column, it was necessary that those hundreds of balls be dropped and sacrificed in the middle columns. It is the only way you can get 5 of them to drop into the outer columns due to the laws of probabilty.
Its important to note: You can do this experiment over and over again, and it will have the same predictable stairstepped outcome every time. The law of prbability never fails over the long term.
So although a mathematical probability equation would tell you that it is not impossible for the outer columns to have more beads than the center columns when this experiment is finished...it will not happen no matter how many times your run this experiment. The outcome will be predictably the same every time.
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Post by rational on Dec 3, 2015 10:57:26 GMT -5
You are wrong about the law of probability. Enough experiments have been done on this. I've been witness to one. The law of probability always rules. You can attempt to keep isolating it to one and talk about the one by itself, but when you do that 1000 times, you no longer have just one, you have a 1000. The law of probability would then be applicable to 1000, not just one like you keep trying to do. Surely you know why the casinos in Vegas make money year end, year out - so long as they have enough volume? Thats right. Because the laws of probability always work. This horse has been beat enough. If you rolled a fair die and noted the number of rolls it took to get to a '6' 166 times, probability would show that the range of possible results would be from 166 to infinity. If you plotted the results the graph would be the familiar bell curve. It would be asymmetrical because the probability does exist that 166 '6' could be rolled consecutively and, on the other end, the probability does exist that to get 166 '6's might require an infinite number of throws. The center of the curve, the most frequent result, would be 1000 with a probability of 1. The probability of the outcome of any number of throws is the result of the probabilities of each individual throw. It seems that you are looking at the 1000 throw situation as having a single probability of producing 166 '6's. Because the 1000 throw situation is made up of 1000 individual events, each having a fixed probability, I think the 'law' you are referring to is the law of total probability. In this case it is trivial because all of the events in the probability space have the same probability. You have to remember that the possibility of 166 '6's showing up in the first 500 throws has the same probability that it will take 1500 throws to get 166 '6's. Casinos do not make their money on probability. The probability is fixed. They make their money by setting odds that are advantageous to the house. For example, if I tell you that if you give me $1 I will give you $5 if you roll the die and get a '6' I have set the odds in my favor. The probability is unchanged. Roulette offers 1:1 odds on the BLACK/RED bet and make their money when the hit is GREEN. Casinos also make money by depending on the ignorance of the player. Watch players in games of chance continue to play because they feel their machine is "due". Of course, if the games are fair and without limit any player that has enough resources can beat the casino.
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Post by jondough on Dec 3, 2015 11:13:58 GMT -5
You are wrong about the law of probability. Enough experiments have been done on this. I've been witness to one. The law of probability always rules. You can attempt to keep isolating it to one and talk about the one by itself, but when you do that 1000 times, you no longer have just one, you have a 1000. The law of probability would then be applicable to 1000, not just one like you keep trying to do. Surely you know why the casinos in Vegas make money year end, year out - so long as they have enough volume? Thats right. Because the laws of probability always work. This horse has been beat enough. If you rolled a fair die and noted the number of rolls it took to get to a '6' 166 times, probability would show that the range of possible results would be from 166 to infinity. If you plotted the results the graph would be the familiar bell curve. It would be asymmetrical because the probability does exist that 166 '6' could be rolled consecutively and, on the other end, the probability does exist that to get 166 '6's might require an infinite number of throws. The center of the curve, the most frequent result, would be 1000 with a probability of 1. The probability of the outcome of any number of throws is the result of the probabilities of each individual throw. It seems that you are looking at the 1000 throw situation as having a single probability of producing 166 '6's. Because the 1000 throw situation is made up of 1000 individual events, each having a fixed probability, I think the 'law' you are referring to is the law of total probability. In this case it is trivial because all of the events in the probability space have the same probability. You have to remember that the possibility of 166 '6's showing up in the first 500 throws has the same probability that it will take 1500 throws to get 166 '6's. Casinos do not make their money on probability. The probability is fixed. They make their money by setting odds that are advantageous to the house. For example, if I tell you that if you give me $1 I will give you $5 if you roll the die and get a '6' I have set the odds in my favor. The probability is unchanged. Roulette offers 1:1 odds on the BLACK/RED bet and make their money when the hit is GREEN. Casinos also make money by depending on the ignorance of the player. Watch players in games of chance continue to play because they feel their machine is "due". Of course, if the games are fair and without limit any player that has enough resources can beat the casino. The above probability machine, and my afterward post best expresses my point. Thanks;
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Post by rational on Dec 3, 2015 13:44:54 GMT -5
So my original point was (using this machine as an example) in order to get 5 balls in the outer column, it was necessary that those hundreds of balls be dropped and sacrificed in the middle columns. It is the only way you can get 5 of them to drop into the outer columns due to the laws of probabilty. And this is where you are still in error. This is just like rolling a die. Each ball represents a single throw. Each ball, assuming they are dropped slowly enough so they do not interfere with each other, has a probability, dictated by the physics of the machine, of which column the ball will fall into. You drop the first ball and it falls into the end column. That is a possibility predicted by the probability of the physics of the system. You drop a second ball and it also falls into the first column. You know this is possible because it happened to the first ball and the second ball is governed by the same probability. You then drop the third ball and it also ends up in the end column. Etc. There is no reason to that there have to be sacrificial balls in order to fill the end column. This is not a law of probability. It is a way to demonstrate the results of a number of trials. Your error is in believing that what has happen in the past somehow influences the outcome of successive trials. Given the knowns there is also a probability that the beads would fall and create a parabola. What you have said at the start of the above paragraph is true but then you contradicted yourself at the end. If the probability exists for the end columns to end up with more beads than the center then if you run the test enough times you cannot possibly say it will not happen.
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Post by jondough on Dec 3, 2015 15:09:22 GMT -5
I disagree, but don't have the time nor the desire to continue to beat this dead horse.
Just keep re-reading my post every time you respond. That is my answer.
Thank you
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Post by rational on Dec 3, 2015 16:39:36 GMT -5
The above probability machine, and my afterward post best expresses my point. Thanks; It is not a probability machine. It is the equivalent of a graphing calculator - it displays the the outcome of multiple probabilities. What it does not show is how the columns were filled, the order in which the beads dropped. Despite your claim that the beads with the highest probability, the beads in the center, have to be dropped (sacrificed) in order for the end columns to be filled, what the video clip showed was the standard distribution of all possible probabilities in the set of variables being considered. It is possible that the first 5 beads dropped were in the end column.
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Post by jondough on Dec 3, 2015 16:52:17 GMT -5
maybe, but probability not
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Post by xna on Dec 3, 2015 18:06:07 GMT -5
Had he died after the first failure nothing would have been contributed. You see, the discussion was regarding the evolutionary failures. The genetic material was not passed forward so there was no contribution to future organisms. If he was successful because of an evolutionary change to his chromosomes and produced offspring those traits would possibly be passed forward. But then this would not be a dead end. However, if the evolved genetic trait that made him successful also made him sterile it would be a dead end and the positive change would not contribute anything towards future generations. Another way to look at it. The law of probability; You are rolling a dice in an attempt to get a 6. It takes you 5 rolls to get the 6. Were the first 4 rolls necessary? Because of the laws of probability, the answer would be yes.In other words, the failures you refer to were in fact necessary to obtain the final results. The failures were contributory. Each single role of a die is independent of any other role. Probabilities change in cases of "without replacement" ie a diminishing number of possibilities. Some probability questions are counterintuitive like the birthday problem, where for a class of 70 their is a 99.9% probability that two people share the same birthday.
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Post by Gene on Dec 4, 2015 12:01:26 GMT -5
You are wrong about the law of probability. Enough experiments have been done on this. I've been witness to one. The law of probability always rules. You can attempt to keep isolating it to one and talk about the one by itself, but when you do that 1000 times, you no longer have just one, you have a 1000. The law of probability would then be applicable to 1000, not just one like you keep trying to do. Surely you know why the casinos in Vegas make money year end, year out - so long as they have enough volume? Thats right. Because the laws of probability always work. This horse has been beat enough. Perhaps you are thinking in terms of averages rather than probability law? If you roll a dice 3 times the probability of rolling a 6 every time is 1/6 x 1/6 x 1/6. I.e (1/6)^3. If you roll your dice 166 times the probability of rolling 166 consecutive 6’s (although low) is non-zero. The probability is (1/6)^166. Dice rolls are always independent events. It does not matter if a dice has been rolled 0 times 1 time or 1000 times. Each and every roll is independent of the previous roll and the subsequent roll. The probability of any number turning up on a regular 6 sided dice throw is always 1/6. The probability is always constant. So, in other words, using a regular 6-sided dice: 1. Q. What is the probability of throwing a 6? A. 1/6 = .17 2. Q. What is the probability of throwing a 6 three times in succession? A. 1/6^3 = .0046 3. Q. After you've thrown a 6 two times in succession, what is the probability of throwing a 6 on the next (3rd) throw? A. 1/6 = .17 4. Q. If that third throw was a 6, what is the probability of the next (4th) throw ALSO being a 6? A. 1/6 = .17
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hberry
Senior Member
Posts: 743
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Post by hberry on Dec 4, 2015 12:19:24 GMT -5
This whole discussion on probability reminds of my current favorite t shirt saying: "Math is all fun and games until someone tries to divide by zero."
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Post by xna on Dec 4, 2015 12:50:18 GMT -5
So, in other words, using a regular 6-sided dice: 1. Q. What is the probability of throwing a 6? A. 1/6 = .17 2. Q. What is the probability of throwing a 6 three times in succession? A. 1/6^3 = .0046 3. Q. After you've thrown a 6 two times in succession, what is the probability of throwing a 6 on the next (3rd) throw? A. 1/6 = .17 4. Q. If that third throw was a 6, what is the probability of the next (4th) throw ALSO being a 6? A. 1/6 = .17 Yep, that's how I figure it. The probability of rolling the same number n times in a row is (1/6)^n for a six sided "fair die". Each roll is unaffected by the other rolls. A fair die has the same odds on each roll. However, no "perfectly fair die" has every been made. That's why god doesn't play dice.
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Post by xna on Dec 4, 2015 13:02:38 GMT -5
Seems about right
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Post by rational on Dec 4, 2015 16:25:15 GMT -5
So, in other words, using a regular 6-sided dice: 1. Q. What is the probability of throwing a 6? A. 1/6 = .17 2. Q. What is the probability of throwing a 6 three times in succession? A. 1/6^3 = .0046 3. Q. After you've thrown a 6 two times in succession, what is the probability of throwing a 6 on the next (3rd) throw? A. 1/6 = .17 4. Q. If that third throw was a 6, what is the probability of the next (4th) throw ALSO being a 6? A. 1/6 = .17 Yep, that's how I figure it. The probability of rolling the same number n times in a row is (1/6)^n for a six sided "fair die". Each roll is unaffected by the other rolls. A fair die has the same odds on each roll. However, no "perfectly fair die" has every been made. That's why god doesn't play dice. :) A "perfectly fair die" is usually generated by using a random source such as radioactive decay or atmospheric noise. In rethinking the idea that there have to be 'sacrificial' events in order to have events with a low probability happen it would mean that it would be impossible to to throw, for example, 3 '6's in a row.
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Post by xna on Dec 4, 2015 16:56:14 GMT -5
A "perfectly fair die" is usually generated by using a random source such as radioactive decay or atmospheric noise. In rethinking the idea that there have to be 'sacrificial' events in order to have events with a low probability happen it would mean that it would be impossible to to throw, for example, 3 '6's in a row. There was the Global Consciousness Project & but I like the movie The Men Who Stare at Goats youtu.be/itQMALL__bE
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