Question

note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. a bowl contains 10 red balls and 10 blue balls. a woman selects balls at random without looking at them. what is the minimum number of balls she must select to be sure of having at least three blue balls?

Answer 1

Worst case scenario for A) is picking up alternating colors, and thus she can only be sure she holds 3 balls of the same color after 5 pickups.
After pickup 1 and 2, she obviously doesn't have 3 of the same color.
After pickup 3 she may have (2,1) (each number in the bracket stands for the number of balls of a given color).
After pickup 4 she may have (2,2).
After pickup 5 she may have (5,0) or (4,1) or (3,2), hence at least 3 of one of the colors.

Regarding B), worst case scenario is that the first 10 balls are red.. So in order to be sure she has 3 blue balls, she needs to pickup 13 times.