First step back and consider the possibilities given no knowledge whatsoever: For each child the problem constrains to one of two possible sexes and one of sev

First step back and consider the possibilities given no knowledge whatsoever: For each child the problem constrains to one of two possible sexes and one of seven possible days of birth. 2 * 7 = 14 possible sex/day combinations for a single child. (2 * 7) * (2 * 7) = 196 possible sex/day combinations for a pairing of two children. To see why, you could write a program to enumerate all of them, starting with the pairing "Boy/Monday + Boy/Monday", then "Boy/Monday + Boy/Tuesday" and so on until you exhaust all possible options at "Girl/Sunday + Girl/Sunday". You'll see there are 196 options. Now start applying the facts given to us: one of the children is born on a Tuesday (eliminate all possibilities which don't have at least one Tuesday child), and that child is a boy (eliminate all possibilities in which there is not a Tuesday child who is also a boy). This leaves exactly 27 possible cases: Boy/Sunday + Boy/Tuesday, Boy/Monday + Boy/Tuesday, Boy/Tuesday + Boy/Tuesday, Boy/Wednesday + Boy/Tuesday, Boy/Thursday + Boy/Tuesday, Boy/Friday + Boy/Tuesday, Boy/Saturday + Boy/Tuesday, Girl/Sunday + Boy/Tuesday, Girl/Monday + Boy/Tuesday, Girl/Tuesday + Boy/Tuesday, Girl/Wednesday + Boy/Tuesday, Girl/Thursday + Boy/Tuesday, Girl/Friday + Boy/Tuesday, Girl/Saturday + Boy/Tuesday, Boy/Tuesday + Boy/Sunday, Boy/Tuesday + Boy/Monday, Boy/Tuesday + Boy/Wednesday, Boy/Tuesday + Boy/Thursday, Boy/Tuesday + Boy/Friday, Boy/Tuesday + Boy/Saturday, Boy/Tuesday + Girl/Sunday, Boy/Tuesday + Girl/Monday, Boy/Tuesday + Girl/Tuesday, Boy/Tuesday + Girl/Wednesday, Boy/Tuesday + Girl/Thursday, Boy/Tuesday + Girl/Friday, Boy/Tuesday + Girl/Saturday If you count, you'll see that of those 27, there are 13 with two boys and 14 with a boy and a girl. The probability of two boys, given that one child is a boy born on Tuesday, is thus 13/27.