He might be. The question does not say one way or the other.
The idea is that there are 198 posibillities for two children and the day they are born (as in: the first is a boy on a monday the second is a girl on sunday - there are 198 different statements like that). If you go through it you will see that excatly 27 of them contains a boy on a tuesday. Of those 27, 13 had two boys. Each of the events are equally likely - well not in the real world, but it would require a bit more info otherwise. So you end up with 13/27.
A non-numerical version goes as follows. To easen the reading I will use unordered pairs:
There are three sets. A set where the boy on a tuesday is born first, F, one there he is born second, S, and one where there are two boys on a tuesday, B. The S and F are equally large and the number of girl boy pairs are equally large in both (similary for boy boy pairs), but they contain a slightly larger probabillity for boy, girl pairs over boy, boy pairs(because neither S nor F contains two boys on a tuesday - they are in B - but they DO contain the posbillity that it is a boy on a tuesday and a girl on a tuesday). The difference is excatly such that if you add B to e.g. F the numbers of boy, girl pairs are equal to the number of boy, boy pairs. Therefore you will have a slightly larger probabillity for girl, boy pairs (because the number of boy, boy in F+B is equal to the number of boy, girl in F+B, but the number of girl, boy pairs are slightly larger than the number of boy, boy pairs in S).