A bag contains 20 yellow balls, 10 green balls, 5 white balls, 8 black balls, and 1 red ball. How many minimum balls one should pick in order to make sure that he gets at least 2 balls of same color.

Since there are five possible colors you must remove SIX balls to guarantee you have two balls of the same color.

Yes, there is only about at 2.3% change that you will draw the red ball in your first five draws, but this is still a possibility. 5 chances in 210 possibles.

Niel