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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 ab\dfrac {a}{b}, where aa and bb are coprime positive integers, find a+ba+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 17 \dfrac{1}{7} irrespective of gender.

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


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