@dysfun the two children are independent of each other but the statement (in its intended interpretation) is dependent on both children. if you knew which child she was referring to it'd go back to 50%.

given the assumption of decidable binary gender (implicit, required), we're counting values of (gender1, weekday1, gender2, weekday2). there are 14 values with gender1 boy and weekday1 tuesday (7 of which have gender2 girl), while 14 have gender2 boy and weekday2 tuesday (7 of which have gender1 girl). but these sets are not disjoint! they share (boy, tues, boy, tues). so there are 27 consistent values rather than 28, and 14 have the other child a girl. 14/27 is roughly 0.519.