A bag contains 33 balls: 10 blue, 11 red, and 12 green. If a person will select balls at random from the bag without replacement, what is the minimum number of balls that need to be selected in order to be sure that the balls selected include 3 balls of the same color?

Answer 1

This is more of a logic question. Let B = blue, R = red, and G = green. If you choose 3 balls, they COULD be three of the same color, but not necessarily. They could be B,R,G. Four balls could be B,B,R,G. Five balls could be B,B,R,R,G. Six balls could be B,B,R,R,G,G and you would still not have three of the same color. However, if you pick one more ball (seven balls total), you are assured that at least three will be of one color. The answer is seven.