In Q3, you've got 8 possibilities, expressed as (gender of 1st child, gender of 2nd child, which child's gender is written inside the sealed envelope?), each with presumably equal probability:

   1. B B 1
   2. B B 2
   3. B G 1
   4. B G 2
   5. G B 1
   6. G B 2
   7. G G 1
   8. G G 2

Once you open the sealed envelope and it says "girl", it does not become Q1, it becomes a different question:

Q4: "A family has two children. I randomly sampled one of the children and it was a girl. What's the probability both are girls?"

In which case, we're looking at possibilities 4, 5, 7, and 8, and in only 2 of those 4 possibilities are both children girls.

In Q1, you're actually told "A family has two children. I looked at both children and can tell you that at least one of them is a girl. What's the probability that both are girls?". In which case, possibilities 3, 4, 5, 6, 7, 8 are all valid. Only in 2 of those 6 possibilities are both children girls.

So as in_cahoots said in https://news.ycombinator.com/item?id=45053187, it matters whether the person asking looked at both children or just a single one.