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This is ridiculous. Let's do some queries on the world: From all women: (some 3 billion) the ones who have exactly two living children: x matches the ones i

This is ridiculous. Let's do some queries on the world: From all women: (some 3 billion) the ones who have exactly two living children: x matches the ones in which it is true for them to say "One of my children was born on Tuesday.". (this is true or false for every mother that comprises x. y mothers remain (can answer "true" for that question") the ones that can say "both my children were born on Tuesday": z matches are you telling me that sizeof z is 1/14th the sizeof y??? (because for me it is either 1/7 that size or exactly 0 if the correct meaning of "one of" is "exactly one of and not both of")

its_so_on 15y ago
Wait, I think I get it. (Sorry, too late to update). This is indeed ingenious. The key is the step from x to y. The women in x who can say "one of my children was born on Tuesday" are the ones who can say "EITHER my first OR my second child was born on Tuesday"; the initial constraint (when you meet the person) is thus: "women who can say I have exactly 2 children and it is true to say EITHER my first OR my second child was born on a Tuesday"; obviously this is far more than 1/7th. Then the additional constraint "BOTH of them were" is a smaller addition than 1/7th. It's not 1/7th the first time and 1/7th the second time, because the question wasn't "of women who can say they have exactly two children, the number who can say 'my elder child was born on a Tuesday'" and then "of these the women who can say 'my younger child was also born on Tuesday". This would indeed be 1/7th each time. instead y is "EITHER my elder OR my younger child was born on Tuesday". This obviously results in a set that is greater than 1/7th of all women with two children, and, consequently, it is no surprise that there is a correspondingly smaller than 1/7th possibility that both were.
- danparsonson 15y ago
  Bingo :-) I was just racking my brain for a different way to explain it but luckily you got there first! It's a real mind-bender.

its_so_on 15y ago

Wait, I think I get it. (Sorry, too late to update). This is indeed ingenious. The key is the step from x to y. The women in x who can say "one of my children was born on Tuesday" are the ones who can say "EITHER my first OR my second child was born on Tuesday"; the initial constraint (when you meet the person) is thus: "women who can say I have exactly 2 children and it is true to say EITHER my first OR my second child was born on a Tuesday"; obviously this is far more than 1/7th. Then the additional constraint "BOTH of them were" is a smaller addition than 1/7th. It's not 1/7th the first time and 1/7th the second time, because the question wasn't "of women who can say they have exactly two children, the number who can say 'my elder child was born on a Tuesday'" and then "of these the women who can say 'my younger child was also born on Tuesday". This would indeed be 1/7th each time. instead y is "EITHER my elder OR my younger child was born on Tuesday". This obviously results in a set that is greater than 1/7th of all women with two children, and, consequently, it is no surprise that there is a correspondingly smaller than 1/7th possibility that both were.

danparsonson 15y ago
Bingo :-) I was just racking my brain for a different way to explain it but luckily you got there first! It's a real mind-bender.