For the less mathematically minded here is the explanation...
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But in that case why do you not also separate BB into Bb and bB where B is the one that you selected and b isn't? If you do, you get BG GB Bb bB GG for which if one is a boy, then it's 50% that the other is a girl.
I agree with you. It's always 50%. DD needs math instructions.
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The Smiths have two children. Therefore there are four possible configurations. GG GB BG BB Since it is stated that one of the children is a boy, the GG is impossible and is discarded. That leaves... GB BG BB Since you know that one is a boy, there are two options where the other is a Girl, GB and BG, and only one where it can be a biy, BB. Therefore there is a 1 in 3 chance of the other child being a boy. Shimples!
------------------------------------ I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave
Dalek Dave wrote:
GB BG
I don't think these two are different configurations?
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Dalek Dave wrote:
GB BG
I don't think these two are different configurations?
Depends, if you take order as a part of your configuration they are, if not then they are the same.
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I agree with you. It's always 50%. DD needs math instructions.
If you put them in age order, then there are 4 possibilities with (almost) equal probability: GG 25% GB 25% BG 25% BB 25% which, indeed could be compacted to: 2G+0B 25% 1G+1B 50% 0G+2B 25% One of them being a boy rules out the 2G combination. Hence 33%. Probabilities were equal at start, and got changed by adding information. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
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Depends, if you take order as a part of your configuration they are, if not then they are the same.
Yes, but I don's see how that affects probabilities in described situation.
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If you put them in age order, then there are 4 possibilities with (almost) equal probability: GG 25% GB 25% BG 25% BB 25% which, indeed could be compacted to: 2G+0B 25% 1G+1B 50% 0G+2B 25% One of them being a boy rules out the 2G combination. Hence 33%. Probabilities were equal at start, and got changed by adding information. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
I only read formatted code with indentation, so please use PRE tags for code snippets.
I'm not participating in frackin' Q&A, so if you want my opinion, ask away in a real forum (or on my profile page).
D'oh!
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The Smiths have two children. Therefore there are four possible configurations. GG GB BG BB Since it is stated that one of the children is a boy, the GG is impossible and is discarded. That leaves... GB BG BB Since you know that one is a boy, there are two options where the other is a Girl, GB and BG, and only one where it can be a biy, BB. Therefore there is a 1 in 3 chance of the other child being a boy. Shimples!
------------------------------------ I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave
Oh wait, I was going to argue with this (Actually I already did, in the previous thread), but I think I have to agree with it now... But it'd make more sense with one additional statement. You're told that one is a boy, but not which one. So you're not pointing to one child and saying "That one is a boy", but rather still keeping both hidden and just saying that one of them is male. If you identified child #1 as the boy, it becomes 50% for the other being male. A clearer way to state the same problem would be, "They have two children, at least one of which is a boy. What are the chances of both being boys?"
Proud to have finally moved to the A-Ark. Which one are you in?
Author of the Guardians Saga (Sci-Fi/Fantasy novels) -
Oh wait, I was going to argue with this (Actually I already did, in the previous thread), but I think I have to agree with it now... But it'd make more sense with one additional statement. You're told that one is a boy, but not which one. So you're not pointing to one child and saying "That one is a boy", but rather still keeping both hidden and just saying that one of them is male. If you identified child #1 as the boy, it becomes 50% for the other being male. A clearer way to state the same problem would be, "They have two children, at least one of which is a boy. What are the chances of both being boys?"
Proud to have finally moved to the A-Ark. Which one are you in?
Author of the Guardians Saga (Sci-Fi/Fantasy novels)You are essentially correct. The problem as stated, specifically asks for the probability of the other child being a boy, which is, and always will be .5, unless I have a deep misunderstanding of the scale on which quantum entanglement works. :laugh: However, if the question is what is the probability of both being boys, the explanation is correct, but the problem misstated. :suss:
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Oh wait, I was going to argue with this (Actually I already did, in the previous thread), but I think I have to agree with it now... But it'd make more sense with one additional statement. You're told that one is a boy, but not which one. So you're not pointing to one child and saying "That one is a boy", but rather still keeping both hidden and just saying that one of them is male. If you identified child #1 as the boy, it becomes 50% for the other being male. A clearer way to state the same problem would be, "They have two children, at least one of which is a boy. What are the chances of both being boys?"
Proud to have finally moved to the A-Ark. Which one are you in?
Author of the Guardians Saga (Sci-Fi/Fantasy novels)If you assumed that one and only one was a boy, then the probability of the other being a boy would be 0.
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The Smiths have two children. Therefore there are four possible configurations. GG GB BG BB Since it is stated that one of the children is a boy, the GG is impossible and is discarded. That leaves... GB BG BB Since you know that one is a boy, there are two options where the other is a Girl, GB and BG, and only one where it can be a biy, BB. Therefore there is a 1 in 3 chance of the other child being a boy. Shimples!
------------------------------------ I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave
and now Chris has been so kind as to provide a really scientific exposé on the boy-girl matter[^] as well as similar problems. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
I only read formatted code with indentation, so please use PRE tags for code snippets.
I'm not participating in frackin' Q&A, so if you want my opinion, ask away in a real forum (or on my profile page).