Fifty balls numbered 1 through 50 are mixed up in a barrel. how many balls must you draw from the barrel (without looking) to be sure that you have two even-numbered balls?

If you draw only 25 balls, you could draw the 25 odd-numbered balls.  However, there will then be no odd-numbered balls left, so when you draw two more you will be guaranteed to get two even-numbered balls.  Thus, the minimum is 25+2=27 balls.