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Post by rjpageuk on May 30, 2010 20:27:48 GMT
The first table is a bit misleading because of the way the grey boxes are labelled as "fails", but yu have to include the BG and GB in the calculation. Maybe I didnt label them in a clear way but the fails and passes are both things that meet the initial criteria. But the second table is just crazy. Again, we don't know whether the girl-born-on-a-Wednesday is in the first or second child, so we can't rule out the possibility that the second child is a girl born on any day of the week - including Wednesday! Therefore the table should look just like the one at the top. Yeah this is why the table is how it is! The possible combinations in full are: G(Wednesday) + B(any day) [7 combinations] (corresponds to the column cells in grey) G(Wednesday) + G(any day) [7 combinations] (corresponds to the column cells in green) B(any day) + G (Wednesday) [7 combinations] (corresponds to the row cells in grey) G(any day) + G (Wednesday) [7 combinations] (corresponds to the row cells in green). It is important to remember that we have double counted G(Wednesday) + G(Wednesday) here, so the total combinations are: 7 + 7 + 7 + 7 -1 = 27. 13 of these are two girl combinations.
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Post by housesparrow on Jun 2, 2010 6:19:02 GMT
Following a debate on the Madrigal Cyber Lounge, I've now humbly concluded that 50% is right after all. Taking the "Girl born Tuesday " red herring, we have the possible combinations
1st child girl born on Tuesday, second child girl born any day 1st child GBT, second child boy 1st child boy, second child GBT 1st child girl born any day, second child GBT
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Post by rjpageuk on Jun 2, 2010 6:58:21 GMT
Following a debate on the Madrigal Cyber Lounge, I've now humbly concluded that 50% is right after all. Taking the "Girl born Tuesday " red herring, we have the possible combinations 1st child girl born on Tuesday, second child girl born any day 1st child GBT, second child boy 1st child boy, second child GBT 1st child girl born any day, second child GBT What debate over there? Dont listen to them The mistake you have made above is you have double counted GBT and GBT which is included in "1st child girl born on Tuesday, second child girl born any day" and "1st child girl born any day, second child GBT". This removes one of the 28 combos.
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Post by housesparrow on Jun 2, 2010 7:32:45 GMT
Yet that applies also to the answer to the first question, doesn't it, where we ended up with two Boy/girl options? Why can't we come to the same conclusion about that? What we should have done is decide that boy/girl and girl/boy are the same, or count two G/G , G/G options, as the second question allows us to do by identifying the known girl in some way.
(Tuesday is just a way of identifying the known child. The other will have been born on one of the other seven days and it doesn't matter which for the purpose of answering the question. We might as well have identified the child as "one girl with red herring hair")
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Post by rjpageuk on Jun 3, 2010 1:37:25 GMT
Yet that applies also to the answer to the first question, doesn't it, where we ended up with two Boy/girl options? Why can't we come to the same conclusion about that? What we should have done is decide that boy/girl and girl/boy are the same, or count two G/G , G/G options, as the second question allows us to do by identifying the known girl in some way. You can decide that Boy/Girl and Girl/Boy are the same if you wish as long as you take into account the fact that it is twice as likely as Girl/Girl. The tables I posted up should clear up this confusion because they show every combination, each of which is equally likely. The reason why it helps to think of boy/girl as different to girl/boy is because each of these combinations are exactly as likely as girl/girl. You are confusing yourself by worring about order. Just think of every single combination as shown in the tables. They are complete. (Tuesday is just a way of identifying the known child. The other will have been born on one of the other seven days and it doesn't matter which for the purpose of answering the question. We might as well have identified the child as "one girl with red herring hair") Yes, the the likelihood of red herring hair would change the outcome. This can be pretty easily visualised by realising that for the girl/girl combo it is just as likely to have a girl with the attribute you set (red herring hair) as BOTH of the other combos as there are two girls that can possibility have this attribute in the girl/girl combo but only one girl in each of the boy/girl and girl/boy combos. Do not confuse this with the implication that red herring hair/being born on a tuesday makes girls more likely that isnt what is happening here.
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Post by housesparrow on Jun 3, 2010 6:43:39 GMT
So far as the first table is concerned, it works only when the sex of neither child is known.
I still believe that my solution is correct:
1st child Known Girl, second child girl born any day 1st child KG, second child boy 1st child boy, second child KG 1st child girl born any day, second child KG
I wish I had stuck to my original answer of 50%: I should know from all those trivia quizzes never to change my first guess!
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Post by housesparrow on Jun 3, 2010 8:02:10 GMT
As for the second problem...well, I don't fully understand it, but think that one problem is that you have to look at each outcome in isolation from what has gone before.
And if you make the substitute of "girl born on any other day of the week" as the alternative choice for "boy" it answers the question just as fully...and gives a 50% result.
Somehow I don't think we will be convincing each other !
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Post by rjpageuk on Jun 3, 2010 10:26:36 GMT
So far as the first table is concerned, it works only when the sex of neither child is known. I still believe that my solution is correct: 1st child Known Girl, second child girl born any day 1st child KG, second child boy 1st child boy, second child KG 1st child girl born any day, second child KG But the sex of neither child is known! It could be either the first or the second that is a girl, we dont know! You are right to put a lot of importance on this. If the question said "the first child is a girl" then the probability would be 50% as the options would be: GB or BB, but it doesnt. The problem with the list that you posted up here is that the first and the fourth items are the same. Visualise it like I said in the post I answered the first problem originally. Pretend there are 20 familes of two children, you would expect each combination of children to be equally likely so: 20 families: 5 BB, 5 GB, 5 BG, 5 GG. Now ask the BB parents to leave and what is left? 15 familes: 5 GB, 5 BG, 5 GG. Now what is the probability of the familiy having two girls? The answer is 5 / 15 or 1 / 3.
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Post by rjpageuk on Jun 3, 2010 10:31:56 GMT
Somehow I don't think we will be convincing each other ! I hope I can convince you! I was lying in bed tonight and realised a different way to look at the second problem. Imagine something absurdly unlikely - imagine the criteria being a girl born at a specific time on a specific day. Now the problem is completely governed by trying to find such a girl, and because BG and GB each only have 1 girl in them they have the same likelihood of having that property as GG which has 2 girls to have the property, making the answer very close to 50%. In fact the more unlikely the criteria is the closer to 50% you end up getting as the probability.
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Post by rjpageuk on Jun 3, 2010 10:55:39 GMT
I found the thread over on MCL. We can take the discussion to there if you would prefer.
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Post by housesparrow on Jun 3, 2010 11:17:19 GMT
You can try...but I suspect that people have given up over there as well!
As for me...well, I shall leave it for a bit and see if I can come back and make my mind up
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Post by alanseago on Jun 3, 2010 11:58:15 GMT
I think it is time to refer to astrology and magnetic forces. The herring galaxy will be in opposition to the fisherman (Ufilletus) and Uranus will be protuberant.
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Post by housesparrow on Jun 3, 2010 12:02:56 GMT
Alan is a genius. : 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. Alan, am I right? Was this the thinking behind that link?
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Post by alanseago on Jun 3, 2010 12:19:12 GMT
Exactly right Housesparrow, but if you concentrate on the basics it is obvious. Do not be led astray, herring are for eating.
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Post by everso on Jun 3, 2010 12:36:57 GMT
This is getting more like Mornington Crescent.
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Post by alanseago on Jun 3, 2010 13:49:33 GMT
Torrens Street.
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Post by housesparrow on Jun 3, 2010 14:22:30 GMT
Angel
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Post by everso on Jun 3, 2010 15:20:28 GMT
Upminster.
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Post by housesparrow on Jun 3, 2010 16:13:03 GMT
Oh trust you Everso!
Now I'll have to replan my whole strategy.
You are right. It is just like having a girl born on a Tuesday
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Post by alanseago on Jun 3, 2010 16:33:38 GMT
Brick Lane Market
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