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 childr

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.