Here is the answer to the original post.

'G' stands for Girl.

'B' stands for Boy.

'T' stands for Thinnest.

'N' stands for Not-thinnest.

If I just told you I have two children and asked what the odds were that they were both boys the answer would be 1:4 or 20%.

All the possible permutations of children being;

G G

G B

B G

B B

By telling you that one of my children is a boy I obviously increase the odds since the pair of girls is eliminated. At this point a lot of people go wrong because knowing I have one boy they just consider that the other child has to be either a boy or a girl so the odds must be 1:2 or 50% in fact they are 1:3 or 33% e.g.

G B

B G

B B

Now I confuse things by throwing in the information that the boy I mentioned is also my thinnest child. At first this appears to be totally redundant information but in fact something strange happens and it makes a big difference to the odds. Here is the complete table of permutations;

GN GN

GT GN

GN GT

GT GT

BN BN

BT BN

BN BT

BT BT

GN BT

BT GN

GT BT

BT GT

GN BN

BN GN

GT BN

BN GT

Now we can delete all invalid permutations that involve two girls or don't have one male child who is thinnest, this shows that the odds of me having two boy is in fact 1:2 or 50%

BT BN

BN BT

GN BT

BT GN

The strange bit though is that the odds have changed because there are now two rows containing two boys.

Truth tables are very powerful and help avoid mistakes in logic. Unfortunately they rapidly get very large and, as Nick wrote, you run out of margin.