Not what you think

Mr Mister has 2 children. One of these children is a boy who was born on a Tuesday. What is the probability that the other child is a boy?

If this probability can be written as $\dfrac {a}{b}$, where $a$ and $b$ are coprime positive integers, find $a+b$.

Assume that the probability of having a boy is half (if it is not a boy, it is a girl) and the probability of being born on Tuesday is $\dfrac{1}{7}$ irrespective of gender.

Knowing which day one of the children was born is important.