#1




When intuition and math probably look wrong
This brings to mind the sort of advanced thinking that tourney pros may contemplate
when sizing their next bet. It also reminds me of the Monte Hall proposition in 21. zg ........... 
#2




Intuition and math don't look wrong.
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Very sad to see a great forum close. I’ll be at the Blackjack Forum with no name. (qfit.com/bj) 
#3




ZG,
If you read through the comments, you'll realize that the intuition that there's a 50% probability of the other child being the boy is actually correct. The article was mistaken. Here are the true possibilities of the second child being a boy, given that one of the children is a boy (credit from the comments): " First, let's assume birth order does NOT matter, here are the possibilities for the gender of a child: 1) Boy 2) Girl so 50% chance of Boy. If we assume birth order matters, then these are the possible combinations: 1) Boy(known), Boy 2) Boy(known), Girl 3) Boy, Boy(known) 4) Girl, Boy(known) Still 50% chance of Boy. " The article tried to present the answer of 1/3 (33%), which wasn't correct.
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"Chance favors the prepared mind." – Louis Pasteur 
#4




You need to go back and carefully STUDY the article. It presents the answer of 13/27, which is ABSOLUTELY correct.

#5




Sucker,
I was referring to the simpler problem given in the article. I studied the article a bit more, and I still stand by what I said. I will explain myself fully, and please feel free to point out the problem in my logic. ********************* I will use 3 names in my reasoning: John, Matt, Sally. The problem is that the article doesn't take into account that we are "given" that John was born on Tuesday. That is the assumption upfront. We already have John born on Tuesday. We also know that John has a sibling. The article also doesn't take into account that the order in which they are born is not important. So here are my possibilities, given that John is born on a Tuesday: 1. John: Tuesday, Matt: Sunday ... 7. John: Tuesday, Matt: Saturday 8. John: Tuesday, Sally: Sunday ... 14. John: Tuesday, Sally: Saturday. That is 14 possibilities, of which 7 of them have a male sibling (Matt), and 7 of them have a female sibling (Sally). Hence 50%. ******************* Now, regarding the article's logic. If you look at their chart (Dead link: http://www.sciencenews.org/view/download/id/60731/name/WORKING_IT_OUT) you can see that they would consider John and Sally both born on Tuesday as separate events that should be counted twice towards the total. Because their logic is that if John is younger, that's 1 event, and if Sally is younger, that's another event. In that case, yes, their reasoning is correct. However, nowhere in the original problem implies that John and Sally both being born on Tuesday should be separate events, because "what if John is younger, or what if Sally is younger" should imply counting the situation of both John and Sally being born on a Tuesday twice. That is where they are incorrect.
__________________
"Chance favors the prepared mind." – Louis Pasteur 
#6




It's a problem of English. What's confusing is that it is unclear if the "one" used in the sentence represents the number 1, or what Germans would say as "man"  "One eats breakfast in the morning and dinner at night," und so wieder.
In the second sense of the word, there is an increased probability that the second child is also a son born on Tuesday, because of the nonzero and nonexcluded chance his children are identical twins. Barring that, and using this nonexclusive sense of the word "one" the other child is equally likely to be male or female or born on any day of the week. 
#7




Ungenau. I thought the same and gave no more thought to the question. There simply is no reason to attempt to devine the meaning of an imprecise question. Before you answer a question, you must understand it. It sometimes pisses off people that email me questions when my response is more questions. But, precision is important. Otherwise, there can be multiple answers to a question, all conflicting and yet all arguably correct. Just not correct for the person asking the question.
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Very sad to see a great forum close. I’ll be at the Blackjack Forum with no name. (qfit.com/bj) 
#8




My intuition says some of this German looks wrong.

#9




Quote:
For THIS problem, there are exactly THREE possibilities, all of which will occur with equal frequency: 1) The first child is a boy, second child is a girl. 2) The first child is a girl, the second child is a boy. 3) Both children are boys. It's quite clear from this that the chance of two boys can ONLY be 1/3. Quote:
There are 27 equal possibilities, of which only 13 consists of two boys: John: Tuesday Matt: Sunday John: Tuesday Matt: Monday John: Tuesday Matt: Tuesday John: Tuesday Matt: Wednesday John: Tuesday Matt: Thursday John: Tuesday Matt: Friday John: Tuesday Matt: Saturday ******** Matt: Tuesday John: Sunday Matt: Tuesday John: Monday Matt: Tuesday John: Wednesday Matt: Tuesday John: Thursday Matt: Tuesday John: Friday Matt: Tuesday John: Saturday ******** Sally: Sunday John: Tuesday Sally: Monday John: Tuesday Sally: Tuesday John: Tuesday Sally: Wednesday John: Tuesday Sally: Thursday John: Tuesday Sally: Friday John: Tuesday Sally: Saturday John: Tuesday ******** Sally: Sunday Matt: Tuesday Sally: Monday Matt: Tuesday Sally: Tuesday Matt: Tuesday Sally: Wednesday Matt: Tuesday Sally: Thursday Matt: Tuesday Sally: Friday Matt: Tuesday Sally: Saturday Matt: Tuesday Note that the reason that there are only 27 possibilities rather than 28, is the fact that if both boys were born on Tuesday, you can only count that ONCE, rather than twice. So this article did INDEED give the correct answer to BOTH problems; 1/3 for the Two Child Problem, and 13/27 for the second problem. As it turns out, all those mathematical geniuses are right after ALL! If you're still having problems understanding this problem, I would suggest that you "Google" and study a similar problem; the "Monty Hall paradox", which involves the same principles, only much simpler to understand. 
#10




Quote:
1) The first child is a boy, second child is a girl. 2) The first child is a girl, the second child is a boy. 3) The first child is the known boy, second child is a boy. 4) The first child a boy, second child is the known boy. 
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