Super Duper Extra Hard Brainteaser

[ethan]

[ QUOTE ]
What are the chances she has two girls?

[/ QUOTE ]

A woman with 1 will answer "yes" 1% of the time. A woman with two will answer "yes" (1 - 0.99^2 + 0.01^2) = 2% of the time. (0.99^2 is the probability of both girls _not_ being named Sarah. The 0.01^2 is added back in because "Sarah" can't be given to both.)

There are twice as many women with only one girl as there are with two, but they answer yes half as often.

So, the answer's 1/2.

[DMBFan23]

I am done until someone comes and handles this is a way I cannot.

good luck all,
me

[DcifrThs]

now when i first looked at this problem, my gut says that order doesn't matter...but after thinking about it, it wouldn't be a brain teaser b/c then the answer would be 50%...

so order DOES matter and the order of the children (age in this case) affects the answer to the problem...

now what if the woman has fraternal twins and its equiprobable its BG or GB for the fraternal twins...same question...does that make it 50%?

-Barron

[Vince Young]

I still don't understand how #1 is 1/3 instead of 1/2. Are BG and GB not the same thing?

[DMBFan23]

[ QUOTE ]
they're the same from the sense of a set of people (when order doesn't matter) but you have to count them as far as equally likely outcomes are concerned.

think about it this way. I flip a coin twice. what are the odds I get two heads? what are odds I get one heads and one tails, in any order?


[/ QUOTE ]

[sammysusar]

i guess im dumb and have taken too many roids but why is the first answer 1/3. seems to this sucker that there are two possibilities 1 boy and 1 girl or 2 girls both equally likely.

[gaming_mouse]

[ QUOTE ]
I am done until someone comes and handles this is a way I cannot.

good luck all,
me

[/ QUOTE ]



Given the information, here are the possibilities:

B,Sara
Sara,B
G,Sara
Sara, G

Each of these events is is equally likely -- it's chance is .5*.5*.01. The answer is therefore 1/2.

[jason_t]

The answer is 1/2. Here's why. Once we have received the information there is a girl and her name is Sarah, we have four possibilities:

Boy, Girl named Sarah
Girl named Sarah, Boy
Girl, Girl named Sarah
Girl named Sarah, Girl.

All of these possibilities are equally likely and there are two possibilities with the situation we are concerned with. So the answer is 2/4 = 1/2.

For those interested in a Monte Carlo simulation to "check" the results, here is C code to do that.

#include <stdio.h>
#include <stdlib.h>

/* c1, c2 are the children; 0 means girl, 1 means boy
n1, n2 are the names; 0 means Sarah, not 0 means not Sarah
count1 is the number of times both children are girls
count2 is the number of times at least one child is Sarah
we are interested in count1 / count2
*/

#define ITERATES 1000000

int main(int argc, char **argv) {
int i;
int count1, count2;
int c1, c2;
int n1, n2;

count1 = count2 = 0;

srand(time());

for(i = 0; i <= ITERATES; i++) {
n1 = -1;
n2 = -1;
c1 = rand() % 2;
c2 = rand() % 2;
if(c1 == 0) n1 = rand() % 100;

if(c2 == 0 && n1 != 0) n2 = rand() % 100;

if(n1 == 0 || n2 == 0) {
if(c1 == 0 && c2 == 0) count1++;
count2++;
}

}

printf("%d / %d\n", count1, count2);
printf("%f\n", (float) count1/ (float) count2);

return 0;
}

[partygirluk]

[ QUOTE ]

Girl, Girl named Sarah
Girl named Sarah, Girl.

All of these possibilities are equally likely

[/ QUOTE ]

Are they?

What is the probability of girl not named sarah, girl named sarah?

99/200 * 1/200 which is 99/40,000

What is the probability of girl named sarah, girl?

1/200 * 1/2 which is 100/40,000

Where am I going wrong?

[DMBFan23]

[ QUOTE ]
[ QUOTE ]
I am done until someone comes and handles this is a way I cannot.

good luck all,
me

[/ QUOTE ]



Given the information, here are the possibilities:

B,Sara
Sara,B
G,Sara
Sara, G

Each of these events is is equally likely -- it's chance is .5*.5*.01. The answer is therefore 1/2.

[/ QUOTE ]

I disagree. I think [girl named sarah, girl] and [girl, girl named sarah] are subsets of [girl, girl].

also, how can the probability of this be HIGHER than the first example, which is less restrictive?