[suivix]

Since he has two children, you know first off that these are all equal chance historically:

BB BG GB GG

Now since you know the child is a boy, it eliminates the fourth option. So now we have these possibilities:

BB BG GB

In only one of these is the other child a boy, so the chance is 1/3.

[bpm140]

This explanation makes a ton of sense. I get it now. Thank you.

[suivix]

Also I don't think the exact day of birth being Tuesday makes one bit of difference to the gender. For example, if you were to say the known boy was born crying, and the chance of this is 70%, it doesn't affect the gender of the other children. It's just useless trivia.

[jules]

That's not true. It does affect the probability of the other child being a boy just like being born on Tuesday does.