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S2000magician Inner circle Yorba Linda, CA 3465 Posts |
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On 2009-01-16 22:28, Magnus Eisengrim wrote: Why is it implicit that the coin is fair? I'm sorry, but I don't agree with that. It's a simplifying assumption, but to allow the students to base their answers on simplifying assumptions is dangerous. The question is (presumably) supposed to test some sort of knowledge or ability. What is this question testing, then? That if a student assumes that the probability is 50% he can conclude that the probability is 50%? Not a particularly useful skill. Quote:
On 2009-01-16 22:28, Magnus Eisengrim wrote: I'd be OK: I don't talk during performances (plays, movies, what have you). I just wish that my younger son had developed that trait! |
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balducci Loyal user Canada 227 Posts |
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On 2009-01-16 20:04, S2000magician wrote: Something called Bayesian statistics or Bayesian inference is what you are looking for. It uses Bayes' theorem but goes a bit beyond it. You'd begin with a prior assumption of, say, 50/50 for head/tail but use the observed data to update those probabilities. I'm just back from the bar and a little tipsy and I refuse to do the calculations right now, but 5 heads would certainly shift the probabilities to something more in line with your intuition that heads is now more likely than tails. People (I don't mean you) make many claims about how bad statistics is, but most of the time they just don't understand what modern statistics really is about. Yeah, people can lie with statistics but only dishonest lobbyists and politicians do so. Your typical neighborhood, legitimate, professional statistician would not.
Make America Great Again! - Trump in 2020 ... "We're a capitalistic society. I go into business, I don't make it, I go bankrupt. They're not going to bail me out. I've been on welfare and food stamps. Did anyone help me? No." - Craig T. Nelson, actor.
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts |
Balducci, that is precisely his point. I'm suggesting that [it should have been obvious that] the radio guy meant nothing of the kind, that he was using "obvious" assumptions to make the rather simple point that the coin has no memory of the past.
S2000 doesn't seem to agree. Fair enough, I didn't hear the program. The different interpretations of the problem are: S2000 (and presumably Lobowolf:) Ignoring what you normally believe about coins and though experiments using coins, what would these outcomes tell you about the coin and, hence about future outcomes. Eisengrim: Accepting what you normally believe about coins, what does the stated outcome tell you about likely future outcomes. Surely an honourable disagreement. John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
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S2000magician Inner circle Yorba Linda, CA 3465 Posts |
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On 2009-01-16 23:35, balducci wrote: Given 5 heads and 0 tails the Bayesian estimate of the probability of getting a head is 6/7; the Bayesian estimate of the probability of getting a tail is 1/7. Quote:
On 2009-01-16 23:43, Magnus Eisengrim wrote: If it had been merely "the radio guy" (gal, actually) who posed the question, I wouldn't have cared more than a whit: she, presumably, isn't a mathematician. I object to having such a poorly-designed question on an exam which will allow someone to graduate (or prevent someone from graduating) from high school. If a student makes the perfectly reasonable assumption that the coin appears to be biased toward heads, he'll get the wrong answer. (And I still have no idea what that word "theoretical" is supposed to mean in that question.) (I don't know whether this is a multiple-choice test or a fill-in-the-answer test: the woman on the radio didn't offer any answer choices, but that doesn't mean that there weren't any there.) |
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S2000magician Inner circle Yorba Linda, CA 3465 Posts |
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On 2009-01-16 23:43, Magnus Eisengrim wrote: If it had been merely "the radio guy" (gal, actually) who posed the question, I wouldn't have cared more than a whit: she, presumably, isn't a mathematician. I object to having such a poorly-designed question on an exam which will allow someone to graduate (or prevent someone from graduating) from high school. If a student makes the perfectly reasonable assumption that the coin appears to be biased toward heads, he'll get the wrong answer. (And I still have no idea what that word "theoretical" is supposed to mean in that question.) (I don't know whether this is a multiple-choice test or a fill-in-the-answer test: the woman on the radio didn't offer any answer choices, but that doesn't mean that there weren't any there.) |
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts |
S2000, Oh, I misunderstood your point. In that case, I agree completely that such a question should not be on the exam unless either it was open-ended and the markers had some sophistication, or if more information was given.
Somehow, I got the impression that you were annoyed by the mathematics, but your annoyance at the context makes much more sense. John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
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ed rhodes Inner circle Rhode Island 2885 Posts |
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On 2009-01-16 20:04, S2000magician wrote: Unless you can show that the person flipping the coin is affecting it in some way. Then the odds of the coin flip are still 50/50 no matter what the history of the coin flip has been.
"...and if you're too afraid of goin' astray, you won't go anywhere." - Granny Weatherwax
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daffydoug Eternal Order Look mom! I've got 14077 Posts |
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On 2009-01-16 16:27, Doug Higley wrote: That's why I stick with chess. No luck involved!! Nope. It's all determined by skill, and I lose just about every time. But at least there are no surprises..
The difficult must become easy, the easy beautiful and the beautiful magical.
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