I came up with a different answer, based on the summary's wording.
Firstly, the sex of the second child is not determined by the first. Whatever one child is, the other will always be 50% chance of being either.
What we can deduce from the wording is that his other child is not a son born on a tuesday.
We draw a two column, 7 row matrix. The rows are days of the week, and the columns are boy/girl. Write a tick in each cell if that is a valid sex and day for the child. We are left with 14 possibilities. 7 of those are girls (a girl can be born on any day), but only 6 are boys (as according to the wording, only ONE is a son born on tuesday...if the other is a son, it cannot be a tuesday, so we are left with 6 days if it's a boy. We give that probability to the girl column.
Thus we are left with 8 out of 14 chances being a girl, and 6 out of 14 being a boy. In decimal: