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S2000magician Inner circle Yorba Linda, CA 3469 Posts 
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On 20090116 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 20090116 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! 

balducci Loyal user Canada 230 Posts 
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On 20090116 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.
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Magnus Eisengrim Inner circle Sulla placed heads on 1064 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 blooddimmed 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 

S2000magician Inner circle Yorba Linda, CA 3469 Posts 
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On 20090116 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 20090116 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 poorlydesigned 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 multiplechoice test or a fillintheanswer test: the woman on the radio didn't offer any answer choices, but that doesn't mean that there weren't any there.) 

S2000magician Inner circle Yorba Linda, CA 3469 Posts 
Quote:
On 20090116 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 poorlydesigned 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 multiplechoice test or a fillintheanswer test: the woman on the radio didn't offer any answer choices, but that doesn't mean that there weren't any there.) 

Magnus Eisengrim Inner circle Sulla placed heads on 1064 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 openended 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 blooddimmed 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 

ed rhodes Inner circle Rhode Island 2726 Posts 
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On 20090116 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.
"There's no time to lose," I heard her say.
"Catch your dreams before they slip away." "Dying all the time, lose your dreams and you could lose your mind. Ain't life unkind?" 

daffydoug Eternal Order Look mom! I've got 14063 Posts 
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On 20090116 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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