Super Duper Extra Hard Brainteaser
 

I'll open with a well know semi-easy one:

You know that a woman has exactly 2 children. You ask her if she has at least one girl, and she says yes. What's the probability that she has two girls?

Answer in white:

<font color="white"> 1/3 </font>

Now, suppose that 1% of all girls are named Sarah, and that if a mother had two girls that the mother would not name both of them Sarah

You know a woman has exactly 2 children, you ask her if she has a girl named Sarah, she says yes.

What are the chances she has two girls?

Re: Super Duper Extra Hard Brainteaser
 

I'm getting just under 1/5 but I could well be out.

Re: Super Duper Extra Hard Brainteaser
 

For a 140+ IQ you don't seem too confident.

Re: Super Duper Extra Hard Brainteaser
 

I am wrong.

Re: Super Duper Extra Hard Brainteaser
 

i'd say, 1/3

Re: Super Duper Extra Hard Brainteaser
 

I say 1/3 for both, assuming an equal distribution of boys and girls (that a woman is equally likely to have a boy as a girl, not 60/40 or 55/45 or whatever it is in reality).

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
For a 140+ IQ you don't seem too confident.

[/ QUOTE ]

Should a person with 140+ IQ necessarily be confident?

Re: Super Duper Extra Hard Brainteaser
 

</font><blockquote><font class="small">In risposta di:</font><hr />
</font><blockquote><font class="small">In risposta di:</font><hr />
For a 140+ IQ you don't seem too confident.

[/ QUOTE ]

Should a person with 140+ IQ necessarily be confident?

[/ QUOTE ]

no

Re: Super Duper Extra Hard Brainteaser
 

Now I'm getting 199/399, but still not sure. Give me 5 mins.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
[ QUOTE ]
For a 140+ IQ you don't seem too confident.

[/ QUOTE ]

Should a person with 140+ IQ necessarily be confident?

[/ QUOTE ]

in his ability to figure out this xtra hard brain teaser?....yes!!

Re: Super Duper Extra Hard Brainteaser
 

The intuitive answer is 1/3 btw, I just need to make sure my maths coincides with it [img]/images/graemlins/smile.gif[/img]

Re: Super Duper Extra Hard Brainteaser
 

without thinking- 1/3
with some crazy miracle thinking- 31%

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
For a 140+ IQ you don't seem too confident.

[/ QUOTE ]

Should a person with 140+ IQ necessarily be confident?

[/ QUOTE ]

in his ability to figure out this xtra hard brain teaser?....yes!!

[/ QUOTE ]

this is not an xtra hard brain teaser, this is a

Super Duper Extra Hard Brainteaser

Re: Super Duper Extra Hard Brainteaser
 

Still getting 199/399 but my logic gut is not confident [img]/images/graemlins/smile.gif[/img]

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
without thinking- 1/3
with some crazy miracle thinking- 31%

[/ QUOTE ]
ok my last crazy miracle thinking guess is 50%
i want credit if any of those are correct [img]/images/graemlins/cool.gif[/img] actually if 1/3 isnt correct, i think 50% is
[img]/images/graemlins/cool.gif[/img]

Re: Super Duper Extra Hard Brainteaser
 

screw it, im going with %50

Re: Super Duper Extra Hard Brainteaser
 

theres 50 girls in the GG pile and 50 girls in the BG/GB pile
shes got at least one of those girls.
50-50! no?

Re: Super Duper Extra Hard Brainteaser
 

in case anyone is waiting for an answer, i don't know, i'm trying to work it out now, this is similar to something my friend asked me a while ago, and i think i figured out the answer to his question, but haven't yet got one for this one

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
in case anyone is waiting for an answer, i don't know, i'm trying to work it out now, this is similar to something my friend asked me a while ago, and i think i figured out the answer to his question, but haven't yet got one for this one

[/ QUOTE ]
you bastard. youre not allowed to ask brain teasers and not mention you dont know the answer already.MFer!! [img]/images/graemlins/cool.gif[/img]
that being said, nodody knows yet if im an idiot or not with my 50% answer!!

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
Now I'm getting 199/399, but still not sure. Give me 5 mins.

[/ QUOTE ]

yah i'm pretty sure this is right

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
[ QUOTE ]
in case anyone is waiting for an answer, i don't know, i'm trying to work it out now, this is similar to something my friend asked me a while ago, and i think i figured out the answer to his question, but haven't yet got one for this one

[/ QUOTE ]
you bastard. youre not allowed to ask brain teasers and not mention you dont know the answer already.MFer!! [img]/images/graemlins/cool.gif[/img]
that being said, nodody knows yet if im an idiot or not with my 50% answer!!

[/ QUOTE ]

[img]/images/graemlins/grin.gif[/img] in my defense I thought I knew the answer, but this is slightly different to another problem I solved, and then I did feel a little bit bad for people guessing when I realized i didn't know the answer, and then i thought it was a little funny

Re: Super Duper Extra Hard Brainteaser
 

I really don't see how the second question is any different then the first. It doesn't seem to matter that the girls name is sarah. I think that info is just provided to confuse you.

Correct me if I'm wrong, but if there are two kids and your using a 50/50 breakdown between girls and boys, then the 4 possiblities are BB BG GB and GG. We know she has a girl, so there are three remaining possibilities. BG GB and GG. All three of which are equally possible. Therefore 1/3 of the time its GG.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
I really don't see how the second question is any different then the first. It doesn't seem to matter that the girls name is sarah. I think that info is just provided to confuse you.

Correct me if I'm wrong, but if there are two kids and your using a 50/50 breakdown between girls and boys, then the 4 possiblities are BB BG GB and GG. We know she has a girl, so there are three remaining possibilities. BG GB and GG. All three of which are equally possible. Therefore 1/3 of the time its GG.

[/ QUOTE ]
This is exactly what I'm saying, but that could all just be an effect of my post-Chipotle haze.

Re: Super Duper Extra Hard Brainteaser
 

I got 199/399 too.

P(G, B) = P(B, G) = 1/4.
Probability of G being named Sarah is 1%.
So given she has two children, 1/100 * 2/4 = 2/400 she has exactly one girl named Sarah.

P(G, G) = 1/4.
First girl named Sarah happens 1/100 times.
If the first girl isn't named Sarah, then the next one will be named Sarah 1/100 times. Probability of this is 99/100 * 1/100.

Probability of her having two girls, one of which is named Sarah is 1/4 * (1/100 + 99/100 * 1/100) = 199/40000.

So probability of her having two girls, given she has one named Sarah, is:

199/40000 / (199/40000 + 2/400) = 199/399.

Either I am missing something or that wasn't a super duper extra hard brainteaser. Just a simple math problem.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
This is exactly what I'm saying, but that could all be just an effect of my post-Chipotle haze.


[/ QUOTE ]

Well I just finished off some Taco Bell, so what do I know.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
We know she has a girl, so there are three remaining possibilities. BG GB and GG. All three of which are equally possible. Therefore 1/3 of the time its GG.

[/ QUOTE ]

Do you think the italicised bit is true given that you know she has a Sarah?

Re: Super Duper Extra Hard Brainteaser
 

i'm re-submitting my answer after deleting it.

there are 3 piles of options.
B = boy
G = girl

BB GG GB

i dont' think that the 1% has anything to do with the problem. once you know that you have a girl, regardless of name...you end up with the two groups: GG (1/3rd chance) and GB (2/3rd chance). the BG group has twice as many people as the GG group, there are the same number of girls in each. which would mean 1/2 chance there is two girls with one named sarah and 1/2 chance there is 1 girl and she is named sarah.

totally wrong?

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
[ QUOTE ]
Now I'm getting 199/399, but still not sure. Give me 5 mins.

[/ QUOTE ]

yah i'm pretty sure this is right

[/ QUOTE ]
whats wrong with 50%?

Re: Super Duper Extra Hard Brainteaser
 

what your saying seems to make sense, and it'd be weird if it wasn't 1/3, but the way i see it before talking to the woman this is true:

boy/sarah with probability 1/200
non-sarah girl/sarah with probability 199/40000

and various other combinations without sarah in it

so after you find out she has a girl named sarah, you know it's one of these two possibilities, and hence you get the 199/399 number

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
there are 3 piles of options.
B = boy
G = girl

BB GG GB

i dont' think that the 1% has anything to do with the problem. once you know that you have a girl, regardless of name...you end up with the two groups: GG (1/3rd chance) and GB (2/3rd chance). since you are twice as likely to find a girl named sarah in the GG group, wouldn't it be twice as likely that if you find sarah, you have two girls? that bumps the GG group to be even with the BG group. which would mean 1/2 chance there is two girls with one named sarah and 1/2 chance there is 1 girl and she is named sarah.

totally wrong?

[/ QUOTE ]

Almost right.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
I got 199/399 too.

P(G, B) = P(B, G) = 1/4.
Probability of G being named Sarah is 1%.
So given she has two children, 1/100 * 2/4 = 2/400 she has exactly one girl named Sarah.

P(G, G) = 1/4.
First girl named Sarah happens 1/100 times.
If the first girl isn't named Sarah, then the next one will be named Sarah 1/100 times. Probability of this is 99/100 * 1/100.

Probability of her having two girls, one of which is named Sarah is 1/4 * (1/100 + 99/100 * 1/100) = 199/40000.

So probability of her having two girls, given she has one named Sarah, is:

199/40000 / (199/40000 + 2/400) = 199/399.

Either I am missing something or that wasn't a super duper extra hard brainteaser. Just a simple math problem.

[/ QUOTE ]
This was my answer 1b, but I think I'm gonna stick with my 1a, which is that the Sarah crap is all a line of bull and the answer is 1/3. In my view, this is somewhat similar to the Let's Make A Deal puzzle we just talked about but with the random door picking in the second round.

In the end, I think all these other calculations would be necessary if the answer to whether or not she had a child named Sarah was no. Then you have to worry about whether or not she has a girl but her name just isn't Sarah. Once the answer to this question is yes, it's essentially the same as the first puzzle - she just told you she has a girl and that's all you need to know.

Re: Super Duper Extra Hard Brainteaser
 

It doesn't matter that the girls named sarah.

Besides, you know her name is sara. The probabitly of this woman haveing a girl named sara is 100%

Re: Super Duper Extra Hard Brainteaser
 

i think it's got something to do with the fact that had she had a girl but not one named sarah this situation would not take place

maybe, i dunno, just throwin something out there

Re: Super Duper Extra Hard Brainteaser
 

It's 1/3 right? It's the same as the first problem, who cares what the 1st girl's name is?

Re: Super Duper Extra Hard Brainteaser
 

Chew on this.

Easy problem 1:

What is probability that a mother of 2 has a girl? (Answer in white below)

<font color="white"> 3/4 </font>

Super duper hard problem:

99 per cent of girls like Barbie. You ask a mother of two whether she has a daughter who likes barbie and she says no. What is the probability that she has a daughter? Still 3/4?

Re: Super Duper Extra Hard Brainteaser
 

Wait a second, Are we sure that the answer to the first question is 1/3.

We know that one kid is a girl. the other kid is 50/50, Boy or girl. So 1/2 GB and 1/2 GG.

Both answers are 1/2

Re: Super Duper Extra Hard Brainteaser
 

nah, I'm 95% sure it's 199/399

and 99% original brain teaser is 1/3

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
Wait a second, Are we sure that the answer to the first question is 1/3.

We know that one kid is a girl. the other kid is 50/50, Boy or girl. So 1/2 GB and 1/2 GG.

Both answers are 1/2

[/ QUOTE ]
We're sure. There are four equally possible combinations of children:

BB BG GB GG

By her answering that she does have a girl, that eliminates the first possibility and leaves three remaining. We're now down to three equally possible combinations, of which GG is one:

BG GB and GG

There is a 1/3 chance that the answer is GG.

Re: Super Duper Extra Hard Brainteaser
 

Note that if her answer were "yes, my second child is a girl" or "yes, my first child is a girl" then it would be 50/50 that both her children are girls.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
I'll open with a well know semi-easy one:

You know that a woman has exactly 2 children. You ask her if she has at least one girl, and she says yes. What's the probability that she has two girls?

Answer in white:

<font color="white"> 1/3 </font>

Now, suppose that 1% of all girls are named Sarah, and that if a mother had two girls that the mother would not name both of them Sarah

You know a woman has exactly 2 children, you ask her if she has a girl named Sarah, she says yes.

What are the chances she has two girls?

[/ QUOTE ]

the answer isn't 1/3. we're drawing from 99% of the sample of girls, but 100% of the sample of boys. knowing that the second girl is NOT a sarah means that 1% of girls are unavailable for us to grab.

so say we have 99 girls and 100 boys, and we want to know the probability, given that one is a girl named sarah, that the other is a girl.

overall we can have

G, B
B, G
G, G

given that we have at least one girl. there are 100 ways to choose the boy in case 1, 100 ways to choose the boy in case 2, and 99 ways to choose the girl in case 3. so, I get 99/300.

initially it looks like conditional probability reduces this problem to the first one, but the "sarah stipulation" controls the sampling of the SECOND girl, not the sarah that we know to exist.