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On A Similar Theme - Probability Again
I remember reading about a problem which went something like this:
Mr Smith has a daughter named Tallulah. What is the probability of his other child being a girl?
The answer was very surprising and counter-intuitive and not the same as the answer in Factor-Fiction's related thread, but the author went through every step and it all made sense. Unfortunately, I can't find the book or remember its title. Does anyone recognise this, and tell me the title or author?
Mr Smith has a daughter named Tallulah. What is the probability of his other child being a girl?
The answer was very surprising and counter-intuitive and not the same as the answer in Factor-Fiction's related thread, but the author went through every step and it all made sense. Unfortunately, I can't find the book or remember its title. Does anyone recognise this, and tell me the title or author?
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I don't know the book, but the argument goes something like this.
Mr. Smith has two children (since he has a daughter and "another child"). A priori, he could have:
Girl+Girl
Girl+Boy
Boy+Girl
Boy+Boy
Each of these has a probability of 1/2 x 1/2 = 1/4 (25%). But the middle two (Boy+Girl and Girl+Boy) are the same, so we have:
2 girls = 25%
1 of each = 50%
2 boys = 25%
We know that the "2 boys" option is ruled out, because he has a daughter called Tallulah. So, were are left with "1 of each" or "2 girls". The probability of "1 of each" is twice as high as "2 girls". So, *given* that he has a daughter called Tallulah, there's only a 1/3 chance (33.3%) that his other child is a girl.
Mr. Smith has two children (since he has a daughter and "another child"). A priori, he could have:
Girl+Girl
Girl+Boy
Boy+Girl
Boy+Boy
Each of these has a probability of 1/2 x 1/2 = 1/4 (25%). But the middle two (Boy+Girl and Girl+Boy) are the same, so we have:
2 girls = 25%
1 of each = 50%
2 boys = 25%
We know that the "2 boys" option is ruled out, because he has a daughter called Tallulah. So, were are left with "1 of each" or "2 girls". The probability of "1 of each" is twice as high as "2 girls". So, *given* that he has a daughter called Tallulah, there's only a 1/3 chance (33.3%) that his other child is a girl.
Paul, that argument works when we don't know the name of the girl. There is a thread on that subject elsewhere on AB. The point is that knowing the unusual name of one of the children changes the probability of the other child being a girl to 1/2. See the link I posted at 3.40 on Thursday 30th Nov.
Incidentally, for others interested, I remember where I read the argument for the first time. It was a book called The Drunkard's Walk, and the girl in the problem is called Florida (as in my other link) not Tallulah. (My memory!)
The author explains it in a simpler way. You can see here by going to page 112 of Amazon's Look Inside function. (Hopefully)
http://
Incidentally, for others interested, I remember where I read the argument for the first time. It was a book called The Drunkard's Walk, and the girl in the problem is called Florida (as in my other link) not Tallulah. (My memory!)
The author explains it in a simpler way. You can see here by going to page 112 of Amazon's Look Inside function. (Hopefully)
http://
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