For the less mathematically minded here is the explanation...
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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
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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
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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
I don't get it GB BG BB is actually BG BB right? since GB and BG is same? so it's 1 in 2 that other child is a boy
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I don't get it GB BG BB is actually BG BB right? since GB and BG is same? so it's 1 in 2 that other child is a boy
No. If you have a boy then a girl, it is not the same as a girl then a boy.
------------------------------------ I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave
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No. If you have a boy then a girl, it is not the same as a girl then a boy.
------------------------------------ I will never again mention that I was the poster of the One Millionth Lounge Post, nor that it was complete drivel. Dalek Dave
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.
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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).