The Tuesday Birthday Problem

I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?
The first thing you think is “What has Tuesday got to do with it?” Well, it has everything to do with it.
Red means “outside the reference class”. Yellow means “in the reference class but not boy-boy”. Green means “inside the reference class and boy-boy”.
Boy-boy in the reference class occurs with probability Green / (Green + Yellow) or 13 /27