So you want a headache:
Brain teaser
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Try looking up the definition of a paradox - it isn't one
Ahem..........
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox
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No, it's just down to probability.
There are four possible combinations of children:
Girl/Girl
Girl/Boy
Boy/Girl
Boy/Boy
If you say one of them is a boy, it leaves three possible situations, one of which results in two boys. Therefore 1/3 chance of there being two boys.
The Tuesday bit is what makes it 13/27, but that's more complex and I can't be bothered typing it.
I read this but i don't understand.
In what way is Girl/Boy a different combination to Boy/Girl.
If we know one is a boy then the other is either a boy OR a girl. The order they were born in doesn't come into it...does it?
You can test with coin tosses. Start the test with the first flip being a boy as in this case you already know the results of the first flip, it's a boy every time. Now flip for the 2nd child. It's always a 50/50 chance for what sex the 2nd child ends up as even if the first results is a boy every single time.
Because it is a different combination. If you have two children it isn't:
33% Boy/Boy
33% Boy/Girl
33% Girl/Girl
It's:
25% Boy/Boy
25% Boy/Girl
25% Girl/Boy
25% Girl/Girl
Therefore when you say "one is a boy", there are three situations where it is possible, and one of those involves both being a boy.
Here's a similar one you may have seen before:
http://en.wikipedia.org/wiki/Monty_Hall_problem
Trust me, I'm right.
think of a question like
you pick ten couples with two kids at random how many couples will have 2 boys?
combinations
b/b
g/g
g/b
b/g
25% will have two boys
if you did
g/g
b/b
g/b
you would have 33.3% which is incorrect
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I see. So because we don't know if the boy is older or younger then we have to assume it could be either. That does make sense. Thanks
I have a girl and my wife is pregnant with our second and for a minute i was thinking the chances were not 50/50! It's too late on a monday for things like this.
The point of it is that it isn't intuitive... it makes you think about it. Most people at first glance will think it's a 50/50 chance.
Correct
Correct but unrelated.
- Flip once, record the result. Flip a second time, record the result.
- Collate this data and group by combination of Girl/Girl, Boy/Girl, Girl/Boy and Boy/Boy.
- Remove Girl/Girl from the results as it is unrelated to the question. Of what you have left, 1/3 will be Boy/Boy and 2/3 will be Boy/Girl or Girl/Boy.
That is incorrect as you already know one result. That means the Girl/Girl outcome is impossible and should not be listed. Knowing one result has no impact on the 2nd result anyway. You can have 6 sons already and the 7th baby due is a 50/50 chance of boy or girl.
The girl/girl outcome isn't included in the calculation of it being 1/3 chance, I was just demonstrating why Girl/Boy and Boy/Girl both need to be included.
You do not know the order of the children. If the question was "my youngest child is a son, what is the chance I have two sons" then the answer would be 1/2. You do not know the order, which adds the Girl/Boy combination and makes the possibility 1/3.
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I don't care what Wikipedia calls it
par·a·dox
[par-uh-doks]Show IPA
noun 1. a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth.
2. a self-contradictory and false proposition.
3. any person, thing, or situation exhibiting an apparently contradictory nature.
4. an opinion or statement contrary to commonly accepted opinion.
There is no contradiction - there is a simple and finite answer to the question. What people with an inproper understanding of statistics deam to be the correct answer is quite simply not correct, thus no paradox.
Plus the examples in the Wiki article are different from the question in the OP, it's asking for the probability of "both" children and the first question stipulates older/youger which affects the calculation.
No you're not buddy and to quote the Monty Hall problem is just silly - it is completely and utterly unrelated to the question in the OP.
You are not opening up the selection and removing one of the wrong ones after someone has made a choice when you know what the answer is - that intervening act is what shifts the probabilities in the Monty Hall problem - if there were no actions, then the probabilities in the Monty Hall problem would always be 1/3.
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You're linking the two together incorrectly... we're not talking about the probability of "both children being boys", the question is asking for the probability of the "other child being a boy"... the "also" statement is moot as it has no bearing on the mentioned child.
The probability of the "other" child being a boy is 50%... simples.
You do not toss a coin and get heads or tails, then toss again and before the result say the odds are 1/3 or 2/3 for the next result. Surly the same logic apply to child birth. Child birth has no memory there are only two possible outcomes. The other child is a boy or girl hence 50/50.
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It's about the probability of one thing, given another, so the "also" very much does have a bearing on it. You're asking about the chances that one of the children is a son, given that the other is.
This is not about the probability of a future event. It's about the probability of an event that has already occurred, by reference to a known outcome in another previously occurring event.
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No, it's just down to probability.
There are four possible combinations of children:
Girl/Girl
Girl/Boy
Boy/Girl
Boy/Boy
If you say one of them is a boy, it leaves three possible situations, one of which results in two boys. Therefore 1/3 chance of there being two boys.
The Tuesday bit is what makes it 13/27, but that's more complex and I can't be bothered typing it.
From a theoretical POV i believe you are correct in there being 4 options, 1 of which (girl/girl) is cancelled out. Though from a literal POV there in no difference between boy/girl and girl boy, therefore for this example 1 should be eliminated. Leaving 2 possible answers Boy/Boy and Boy/Girl (reverse if needed). Meaning the chances for this example are 50%.
This is my understanding.