Question

Jar has 10 red balls and 10 blue balls, and you have to take balls out of the jar, at random, without looking.



how many balls do you need to take out in order to be sure you are holding at least 3 blue balls?

Answer 1

After picking up 1 and 2, you will not be sure that you have 3 of the same color.

After picking up 3 you may have (2r,1b), (1b, 2r), (3r,0b)

After picking up 4 you may have (2r, 2b),(4r,0b)

After picking up 5 you may have (5r, 0b) or (4r,1b) or (3r,2b), hence at least 3 of one of the colors.

Similarly 6 may be (5r, 1b),(4r, 2b), (6r,0b)

7 may be (6r, 1b),(5r, 2b),(7r,0b)

8 may be (7r, 1b),(6r, 2b),(8r,0b)

9 may be (8r, 1b),(7r, 2b),(9r,0b)

10 may be (9r, 1b),(8r, 2b),(10r,0b)

11 may be (10r, 1b),(9r, 2b)

12 may be (10r, 2b)

Hence you need to pick up at least 13 balls in which in every case you will definitely get at least 3 blue balls.