/sci/ - Science & Math

Uh sweaty, gender/sex is a spectrum. Girls and boys don't exist.

>>12369852
>1: A man has two children, one of which is a boy. What are the odds that the other child is also a boy?
1/2

>2: A man has two children, and the older one is a boy. What are the odds that the other child is also a boy?
1/2

>>12369852
Isn't it 1/3 for both?

>>12369859
Incorrect

>>12369861
Also incorrect

>>12369866
Oh yeah, it's 1/3 for question one and 1/2 for question two.

>>12369862
Nope, it's correct. Since both questions refer to "the other child," the first part of both questions refers to a specific child, not the state of the pair. The genders of each child are independent from each other.

If you had asked about the pair instead of "the other child," then the question would be ambiguous.

is this like a retarded version of the monty hall problem?

>>12369870
Elementary probability problems are so stupid. The only challenge is divining the actual meaning of the question and then all the calculation is trivial. Just give me a rigorously-defined probability space and ask something interesting.

>>12369870
Fuck, I messed it up. Well, it's a retarded paradox anyway and I don't get it

>>12369852
You are a biologist traveling through a rainforest when you are bitten by a venomous snake. Luckily the antidote to this venom is secreted on the back of the male of a certain species of frog native to this rainforest. You know females and males exist in equal proportion, socialize with each other randomly, and are indistinguishable aside from the fact that females croak randomly but males never croak. Amazingly, you see a frog of this species sitting silently in front of you. You then hear a croak and turn around to see a pair of these frogs where the croak came from. Knowing that you only have enough time to run to the lone frog to lick its back or to the pair to lick both their backs, which direction do you run and what is your chance of survival?

>>12369870
Isn't "the other child" the exact same thing as the state of the pair? They refer to the same thing, no?

>>12369876
It's pretty simple. If you only saw one child and it was a boy then you have information about a specific child and the gender of the other child is independent from that info. If your friend told you he saw both children and at least one is a boy then you have information about the pair, not a specific child, and the gender of both children is not independent from that info.

>>12369882
>Isn't "the other child" the exact same thing as the state of the pair?
No, because you can get information about the pair that doesn't refer to a specific child.

>>12369885
How is the gender of the other child not independent from that info? If you flip a coin and it lands on heads then the probability of ut landing on heads again is still 1/2

>>12369888
No more info is given, you know that it's a pair in both cases

>>12369892
>How is the gender of the other child not independent from that info?
What "other child?" In order for "other child" to make sense, the information would have to refer to a specific child in the first place.

If I flip two coins and tell you I counted the number of heads and it's greater than 0, does this tell you anything about a specific coin? No.

>>12369898
I don't get it

>>12369895
The information that was given in the hypothetical I'm talking about doesn't refer to a specific child, it only refers to the state of the pair. I'm not adding information.

>>12369900
Which child is the other child?

>>12369901
If you're not adding information, how can the probability change? The answer is supposed to be 1/3 for the first one and 1/2 for the second one

>>12369906
>If you're not adding information, how can the probability change?
I'm taking away information.

>The answer is supposed to be 1/3 for the first one
No, it's worded incorrectly. See >>12369870

>>12369877
The pair, as it gives 2/3 odds, since there are 4 possible "states" for a pair of frogs (both male, both female, and 2 ways to order them if of different sexes), with one state (both male) eliminated due to the croak. Is this right, or am I retard?
Trick question: I'm a retard for entertaining this thought experiment.

Let's try explaining this a different way. Here are all the states a pair of children can be in, all equally likely:

BB
BG
GB
GG

The distinction between information about a specific child and information only about the pair is simply saying that BB is 1/2 of the states where a specific column is B and 1/3 of the cases where either column is B.

>>12369926
>The pair, as it gives 2/3 odds, since there are 4 possible "states" for a pair of frogs (both male, both female, and 2 ways to order them if of different sexes), with one state (both male) eliminated due to the croak.
Incorrect. You're ignoring that we heard a frog croak. So the states are actually

Fc F
Fc M
M Fc
F Fc

You know how to apply the logic of the boy girl paradox but don't truly understand when it applies.

>this thread

>>12369852 (OP)
>>12369859
>1: A man has two children, one of which is a boy. What are the odds that the other child is also a boy?
2/3

>2: A man has two children, and the older one is a boy. What are the odds that the other child is also a boy?
1/2

>>12370002
>2/3
Incorrect. See >>12369870

>>12369852
>assuming there are only two genders
>assuming boy/girl are 50-50
>assuming there's no correlation between sibling genders

>>12369872
Yes, it's another way to misstate the Monty Hall problem so people get the "incorrect" answer. Not sure if OP is doing it to trip people up so he can feel intellectually superior or if he's simply an idiot.

>>12369892
no. a woman is more likely to have same gender kids.

also, since there is no fair coins, if a coin lands on head, a better guess would be it'll land on head again. if a coin lands on heads 10 times in a row, only a statistician would bet on tail next time - because... theory?

>>12370019
>Every probability question is Monty Hall

>>12369852
0%, both questions state that only one is a boy

>>12370013
"One of which" is not specific. "The older one" is.

>>12370104
>"One of which" is not specific.
It is if it's followed up by a question about "the other child."

>>12370080
Neither say that.

>>12370107
No it isnt. You still dont know if hes talking about child 1 or 2.

>>12370118
If he's taking about 2 children then he can't ask about "the other child."

>>12370148
>If he's taking about 2 children then he can't ask about "the other child."
Hes talking about 1 out of 2 kids. Not 2 kids. And we dont know which kid hes talking about so we take both kids into consideration when calculating the probability.

>>12370271
>Hes talking about 1 out of 2 kids.
Yes, so a specific kid.

>And we dont know which kid hes talking about
It doesn't matter which kid he's talking about since the question is about the other kid.

>so we take both kids into consideration when calculating the probability.
It doesn't matter if you take both kids into account, the gender of the other kid is independent from the first one.

>1: 1/3
BB, BG, GB, GG
Given there must be at least one boy GG is eliminated so
BB, BG, GB
where the outcome of both-boys is BB is 1/3.

>2: 1/2
BB, BG, GB, GG
First chid is B, so GB and GG eliminated so
BB, BG
where the outcome of both boys BB is 1/2.

>>12370312
We dont know if hes talking about the older or younger child so how is it a specific child? Saying the other one still wont specify which child it is hes talking about.

>>12370341
>Given there must be at least one boy GG is eliminated
The question asks about "the other child" so the states are simply

BB
BG

>>12370342
>We dont know if hes talking about the older or younger child so how is it a specific child?
Huh? Why would it matter which one is younger or older? We know it's a specific child because he says "the other child." I don't know why you keep failing to respond to this. You are confusing the question being about a specific child with the question telling us which child is which in relation to some trait. The trait is not relevant, only specificity is.

>>12369852
zero bc i'd abort if it was a girl.