Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
What is the probability of girl named sarah, girl?

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

Where am I going wrong?

[/ QUOTE ]

1/200 * (99/100) * 1/2. They can't both be sarah.

Re: Super Duper Extra Hard Brainteaser
 

jason, by that logic the answer to the first, easier, problem is 1/2, which is wrong.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
[ QUOTE ]
What is the probability of girl named sarah, girl?

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

Where am I going wrong?

[/ QUOTE ]

1/200 * (99/100) * 1/2. They can't both be sarah.

[/ QUOTE ]

Hmm. The probability of the first child being a girl called Sarah is just 1/200 and then the probability of the next one being a girl is 1/2 n'est pas?

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
What is the probability of girl named sarah, girl?

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

Where am I going wrong?

[/ QUOTE ]

1/200 * (99/100) * 1/2. They can't both be sarah.

[/ QUOTE ]

Hmm. The probability of the first child being a girl called Sarah is just 1/200 and then the probability of the next one being a girl is 1/2 n'est pas?

[/ QUOTE ]
Non. Read this. All of it.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
jason, by that logic the answer to the first, easier, problem is 1/2, which is wrong.

[/ QUOTE ]

There are three possibilities once we know there is at least one girl:

girl, girl
boy, girl
girl, boy

Therefore the answer to the first question is 1/3

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
jason, by that logic the answer to the first, easier, problem is 1/2, which is wrong.

[/ QUOTE ]

Wrong, the possibilities in the first question, once we know there is at least one girl are

G, B
B, G
G, G

and all of these are equally likely. So the answer is 1/3.

Re: Super Duper Extra Hard Brainteaser
 

Seems to me that this is only a brainteaser because it induces people to waste a bunch of time with the Sarah red herring when the answer is still 1/3.

Think about it intuitively: If you gathered a population of mothers with two children, at least one of which is a girl, and divided them into subpopulations based on whether they had a child named Sarah, would you expect the subpopulations to have different estimated means on the #ofGirls variable. Basically, the Sarah thing just identifies a subpopulation but shouldn't change any other characteristics.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
Seems to me that this is only a brainteaser because it induces people to waste a bunch of time with the Sarah red herring when the answer is still 1/3.

Think about intuitively: If you gathered a population of mothers with two children, at least one of which is a girl, and divided them into subpopulations based on whether one they had named a child Sarah, would you expect the subpopulations to have different estimated means on the #ofGirls variable. Basically, the Sarah thing just identifies a subpopulation but shouldn't change any other characteristics.

[/ QUOTE ]
Exactly.

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
Seems to me that this is only a brainteaser because it induces people to waste a bunch of time with the Sarah red herring when the answer is still 1/3.

Think about intuitively: If you gathered a population of mothers with two children, at least one of which is a girl, and divided them into subpopulations based on whether one they had named a child Sarah, would you expect the subpopulations to have different estimated means on the #ofGirls variable. Basically, the Sarah thing just identifies a subpopulation but shouldn't change any other characteristics.

[/ QUOTE ]

Think about it like this, it might change your mind: knowing that a women has two girls increases the likelihood that she has a child named Sarah. Conversely, knowing she has a child named Sarah....

Re: Super Duper Extra Hard Brainteaser
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
What is the probability of girl named sarah, girl?

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

Where am I going wrong?

[/ QUOTE ]

1/200 * (99/100) * 1/2. They can't both be sarah.

[/ QUOTE ]

Hmm. The probability of the first child being a girl called Sarah is just 1/200 and then the probability of the next one being a girl is 1/2 n'est pas?

[/ QUOTE ]
Non. Read this. All of it.

[/ QUOTE ]

Please explain which part of what I said was wrong.