At least one boy born on a Tuesday
A family has two children, each independently equally likely to be a boy or a girl, and each equally likely to be born on any of the seven days of the week.
Given that at least one child is a boy born on a Tuesday, what is the probability that both children are boys?
Show a hint
Each child now has equally likely "type" labels. Count the outcomes with at least one boy-born-on-Tuesday, then how many of those have two boys.