4. Think of the worst possible situation.  It's unlikely but possible for you 
to pull out all 28 boys' names in a row, one by one.  Then there would be 
no more boys'; names in the hat. So the next 2 names you would pull out 
MUST be girls' names.  So if you pull out 30 names, you are certain that at
least 2 of them MUST be girl's names. So in the worst possible case you would
have 28 boy's names and 2 girl's names.   

Answer: 30

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5. You only need to pull out 3 for there are only two sexes, so there must be
two of one sex among the three.  They are either 3 of the same sex or two on
one sex and 1 of the other.  So with only 3 names you can be sure of having
2 boys' names or 2 girls' names.

Answer: 3

Edwin