beesonthewhatnow
going deaf for a living
Oh shit.
The second part is not "What is the probability that the other child is a boy" but "What is the probability you have two boys?"
That's where we went wrong, LBJ.
Hall-e-fucking-lujah
Puzzle: I have two children ...
- Thread starter bmd
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Hall-e-fucking-lujah
ymu
Niall Ferguson's deep-cover sock-puppet
Where did you get those probabilities from?
There are 4 equally likely families with two children:
BB
GG
BG
GB
p=1/4 for each possibility
As soon as I know there is at least one boy we have:
BB
BG
GB
There are now only three possibilities, all still equally likely, and only one of them has a second boy.
if you're going to collapse the birth order as irrelevant (which it is), you still have to assign the correct probabilities to each family mix.
If you can't handle the theory, try doing it empirically. Toss some coins and keep records of each pair of throws. Then count how many pairs had a head in them, and how many of these had two heads.
Crispy
The following psytrance is baṉned: All
I can claw back a glimmer of pride by knowing that I was answering the wrong question right, instead of the right question wrong
There's no difference, the problem is the same with both statements. If the other child is a boy then he has two boys, and vice-versa.Oh shit.
The second part is not "What is the probability that the other child is a boy" but "What is the probability you have two boys?"
That's where we went wrong, LBJ.
Plane crashes into the mountain. No survivors.
littlebabyjesus
one of Maxwell's demons
It is the same question, though. You are told one is a boy, so the probability that the other is a boy is the same as the probability that you have two boys.Oh shit.
The second part is not "What is the probability that the other child is a boy" but "What is the probability you have two boys?"
If the other is a girl, you don't have two boys.
If the other is a boy, you do have two boys.
There's a confusion here as to the question being asked. I repeat, this is a question about one child, not two.
beesonthewhatnow
going deaf for a living
I can claw back a glimmer of pride by knowing that I was answering the wrong question right, instead of the right question wrong
You've still lost 7.5 science points though
Crispy
The following psytrance is baṉned: All
It's not, the question is about the probabilty of "two boys"
beesonthewhatnow
going deaf for a living
There is a difference. It is a very important difference, because it gives different answers. This is fairly basic probability theory.
There is confusion here certainly, and it's about 12" from your screen.
ymu
Niall Ferguson's deep-cover sock-puppet
You're right, they are the same question. Where you're wrong is in saying that two-child families with two boys are just as common as two-child families with a boy and a girl. They're not.
Crispy
The following psytrance is baṉned: All
really?There's no difference, the problem is the same with both statements. If the other child is a boy then he has two boys, and vice-versa.
then I might have to restart the failwagon and continue making a fool of myself
littlebabyjesus
one of Maxwell's demons
4 cards, in this case. (BB, BG, GG, GG)
beesonthewhatnow
going deaf for a living
really?
then I might have to restart the failwagon and continue making a fool of myself
You fell off it, slightly hurting yourself in the process. No need to climb back on board and risk further injury
You are confused. "what is the chance the other one is also a boy?" is the same problem as it asks precisely the same question.
littlebabyjesus
one of Maxwell's demons
I have two chlidren.
P(at least 1 boy) = .75
P(two boys) = .25
P(only 1 boy) = .5
I have two children and one is a boy.
BB
BG
GB
You now have to choose an order. Declaring that 'one is a boy' knocks out either BG or GB, because the one declared is not put back into the mix. He is eliminated from your consideration.
P(at least 1 boy) = .75
P(two boys) = .25
P(only 1 boy) = .5
I have two children and one is a boy.
BB
BG
GB
You now have to choose an order. Declaring that 'one is a boy' knocks out either BG or GB, because the one declared is not put back into the mix. He is eliminated from your consideration.
littlebabyjesus
one of Maxwell's demons
ymu
Niall Ferguson's deep-cover sock-puppet
No, they're not. You're not considering the probability of each outcome.
If I have two children then I either had
BB
GG
BG
GB
It's 50/50 that my children are the same sex.
But if you know that one of my children is a boy, I cannot have had two girls. There are now only three possibilities and they are all equally likely. Only one of them has me with two boys.
littlebabyjesus
one of Maxwell's demons
ymu
Niall Ferguson's deep-cover sock-puppet
Declaring birth order irrelevant does not change the probability - it just makes BG twice as likely because you're lumping it in with GB.
If I had BG, then I have one son, not two. If I had GB, then I have one son not two. If I had BB than I have two sons.
beesonthewhatnow
going deaf for a living
ymu
Niall Ferguson's deep-cover sock-puppet
Arrrrgh!!!
I repeat, this is a very well known problem. We're not misinterpreting it - you are.
really?
then I might have to restart the failwagon and continue making a fool of myself
Really no shame, you are thinking about it and there is really awkward territory here.
Allow me to state the problem two different ways
Person 1 "I have two children"
Person 2 "Is one a boy born on a Tuesday?"
Person 1 "yes"
or
Person 1 "I have two children"
Person 2 "What is the sex and day of birth of the eldest child?"
Person 1 "it is a boy born on a Tuesday"
these have different answers. In the latter, it's just 50/50, the second child is indeed just independent.
FridgeMagnet
Administrator
It helps to understand this if you imagine putting the boy behind door 1, and then the other child behind door 2 or door 3, with the other door having a goat behind it.
Crispy
The following psytrance is baṉned: All
poor mother
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