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Post by rjpageuk on Jun 4, 2010 2:45:42 GMT
His link explains, albeit somwhat obscurely, why the table you drew in answer to question one doesn't work! Because once you remove one link in the DNA chain, everything else gets shifted across and a completely different set of amino acids result. So we have to remove the BB option before drawing the table. The BB option is marked as ruled out from prior conditions, and you are right doesnt need to be in the table. I dont really know whats going on in this thread anymore, whether people are joking or not. These maths problems are well known and very old, the answers given are correct and there isnt any dispute over this. Lots of people just have problems understanding them, which is why I am trying to clear up the misunderstandings with loads of different ways of thinking about the problem.
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Post by housesparrow on Jun 4, 2010 6:47:35 GMT
Rob, there seems to be plenty of dispute over this, and not just on the message boards! Have a look at the comments under the New Scientist article. www.newscientist.com/article/dn18950-magic-numbers-a-meeting-of-mathemagical-tricksters.html?full=trueI'm no mathematician but so have a vague idea that there is something not quite right with the one third option. And, quoting from the body of the article itself: "The first thing to remember about probability questions is that everyone finds them mind-bending, even mathematicians."
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Post by rjpageuk on Jun 4, 2010 12:08:29 GMT
Yes I know, I first saw these problems over 10 years ago. The comments on the article are just the same as comments from people in this thread or the one over at MCL (or the various other forums it has been posted on) struggling to understand. Not from anyone who is familiar with these problems.
The misunderstandings just come from a misinterpretation of the question, the comments are from people either doing that or misapplying the maths.
The reason why people misinterpret so much is because the scenario the question raises would not generally come up in any real world scenario.
If the parent picks a random child and then reveals its gender, then the probability of both children being that gender is 50%, but this isnt what has happened in the question. The key difference is that in this question we have been given information about the PAIR of children, not an individual child.
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Post by alanseago on Jun 4, 2010 12:17:25 GMT
The nail on the head rj. I have read (elsewhere) posters discussing the relevance and importance of Tuesday.
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Post by housesparrow on Jun 4, 2010 13:25:32 GMT
Ah - now you have lost me. What is the difference between a parent picking a random child (ie choosing at random one of two) and the question: I have two children. One of them is a girl. What is the probability I have two girls?
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Post by housesparrow on Jun 4, 2010 13:35:02 GMT
I've started reading this, which Ron posted on MCL, and can understand a bit more....but the day is too nice. en.wikipedia.org/wiki/Boy_or_Girl_paradox"understand" is perhaps being a little over-optimistic. Shall I say, I have read a little more!
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Post by alanseago on Jun 4, 2010 13:41:23 GMT
It is simply the difference between an individual child and a series of children. Answer the question asked. On a walking holiday, you come to an unmarked fork in the road. Which is the right road L or R? 50/50 One mile further on you come to another unmarked fork.What are the odds on This One being L or R? 50/50 Do not confuse a single occurrence with a sequence.
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Post by housesparrow on Jun 4, 2010 15:25:46 GMT
If that was in answer to my #64. Alan, it hasn't helped - sorry.
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Post by rjpageuk on Jun 5, 2010 3:26:42 GMT
Ah - now you have lost me. What is the difference between a parent picking a random child (ie choosing at random one of two) and the question: I have two children. One of them is a girl. What is the probability I have two girls? The difference is that if a parent picks a random child and reveals its gender there are now only two combinations of things the other child can be, you are effectively making the question: "I have two children. The youngest of them is a girl. What is the probability I have two girls?" Now the answer is 50%. This is because you have removed one of the three possibilities (BG is now no longer possible, just GB and GG). The gender of the child the question is asking about is not random, it is specifically a girl. I havent even read that wiki article, so no idea if it is helpful but from a cursory browse it appears to be using pretty much the same arguments I have used in this thread already. I know this is difficult to understand. Here is an exercise you can try if you wish that may help you see it. Get a coin and toss it twice and record the results on a bit of paper. Do it about 20 times (ideally more). Discard the results that do not contain at least one head, and count the proportion of the remaining results that are both heads. It will be approx 1/3rd.
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Post by rjpageuk on Jun 5, 2010 3:45:27 GMT
Incidentally, it is a bit of a coincidence but I am reading The Riddle of Scheherazade at the moment as my holiday book and this problem is in there! It is worded a little differently: "A man has two cats. At least one of them is male. What is the probability both are male?" Unfortunately the answer and explanation is fairly short and just a retreat of what I have written previously in here.
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Post by housesparrow on Jun 5, 2010 8:16:49 GMT
Well, I can't keep changing my mind over this, Rob: I'll get a reputation.
But of course, if you accept that as many two child families have two girls as thse who have two boys, and 50% of the total have a girl and a boy, you are right; one third of those with a boy have two boys.
If you begin with the premise that no family has two girls, you get 50%
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Post by alanseago on Jun 5, 2010 12:39:16 GMT
The English Language: I am pregnant, will it be a boy or a girl? 50/50 I am pregnant again, will it be a boy or a girl? 50/50
What are the chances of having six girls? Unknown
What are the chances of a volcanic eruption on Maundy Thursday: discuss, ad nauseum.
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Post by housesparrow on Jun 5, 2010 13:15:55 GMT
I'm finding it fascinating.....
Perhaps I should get out more.
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Post by rjpageuk on Jun 5, 2010 14:10:47 GMT
I'm finding it fascinating..... Perhaps I should get out more. It is fine, I love this stuff, thats why I am reading a book full of them! But of course, if you accept that as many two child families have two girls as thse who have two boys, and 50% of the total have a girl and a boy, you are right; one third of those with a boy have two boys. If you begin with the premise that no family has two girls, you get 50% I dont understand the difference between these two, so why you are happy to accept 1/3rd for one but think it is 1/2 for the other.
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Post by housesparrow on Jun 5, 2010 14:27:30 GMT
I don't.
If the answer is 1/2 for one, it should be 1/2 for the other. Ditto with 1/3.
That's where my head is turning to brawn.
If there is no "known child" in question one, then the answer is one third. You have a family with two children, one of whom is a girl - fine. Of all the families with two children, one quarter will have two girls, one quarter two boys, and the rest a b0y and girl. Right?
But if this family has one girl, who happens to be born on Tuesday/have red hair/turns cartwheels the whole thing shifts?
Odd. I'll chew over it.
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Post by Weyland on Jun 5, 2010 20:06:16 GMT
Unfortunately the answer and explanation is fairly short and just a retreat of what I have written previously in here. Case closed. G, then GB or GG, 50% probability each, and that's that.
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Post by everso on Jun 5, 2010 20:18:30 GMT
I knew something had been missing this week. Weyland's back and he's being all decisive.
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Post by Weyland on Jun 5, 2010 20:23:15 GMT
I knew something had been missing this week. Weyland's back and he's being all decisive. Thank you, Ev, but I'm not quite back yet. Still at friend's place with very swollen ankle. Probably properly back on Monday. Meanwhile -- to hell with the expense -- get your kit off . . . . .
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Post by everso on Jun 5, 2010 20:23:52 GMT
Tsk!
How was London?
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Post by riotgrrl on Jun 5, 2010 20:24:00 GMT
I knew something had been missing this week. Weyland's back and he's being all decisive. Thank you, Ev, but I'm not quite back yet. Still at friend's place with very swollen ankle. Probably properly back on Monday. Meanwhile -- to hell with the expense -- get your kit off . . . . . Behave. This is not a stag party, and Mrs E is not the stripper!
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