Common sense suggests there are only two possible outcomes: TuesdayBoy+Boy, and TuesdayBoy+girl, each with a probability of 1/2.Select all people who have two children, at least one of which is a boy born on Tuesday. Given one of those individuals, what is the probability that their other child is a boy?

But some hard-charging pundit for the other team has gone on to suggest otherwise by creating an outcome space like so:

Mon-Boy Tue-Boy Wed-Boy Thu-Boy Fri-Boy Sat-Boy Sun-Boy Mon-Girl Tue-Girl Wed-Girl Thu-Girl Fri-Girl Sat-Girl Sun-Girl Mon-Boy

XXXXXX

Tue-Boy XXXXXX

XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX Wed-Boy

XXXXXX

Thu-Boy

XXXXXX

Fri-Boy

XXXXXX

Sat-Boy

XXXXXX

Sun-Boy

XXXXXX

Mon-Girl

XXXXXX

Tue-Girl

XXXXXX

Wed-Girl

XXXXXX

Thu-Girl

XXXXXX

Fri-Girl

XXXXXX

Sat-Girl

XXXXXX

Sun-Girl

XXXXXX

From this table of outcomes, 27/196 possible two-child families have at least one Tuesday-Boy. Furthermore, 13/196 outcomes are TuesdayBoy+Boy, while 14/196 outcomes are TuesdayBoy+girl. And I'm willing to believe that drawing a random entry from this outcome space will result in TuesdayBoy+Boy with a probability of 13/196, and TuesdayBoy+Girl with a probability of 14/196.

But I'm pretty sure the assessment that this represents the quoted question accurately is in error. And I think the mechanism of selecting the subset of qualified results is the source of that error.

Any help?