A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?
- (a) 17
- (b) 16 ✓ UPSC's answer
- (c) 13
- (d) 11
Why the answer is (b)
• To find the minimum number of balls needed to guarantee at least one of each color, we must consider the worst-case scenario.
• In the worst case, you pick all balls of the two most numerous colors before picking the first ball of the third color.
• The two most numerous colors are green (8 balls) and white (7 balls).
• Picking all 8 green and all 7 white balls results in 15 balls with no red balls.
• The next ball picked (the 16th) must be red, ensuring at least one ball of each color is in hand.
Why the other options are wrong
- (a) 17
- 17 is not the minimum because the guarantee is achieved at 16 balls.
- (c) 13
- 13 is insufficient because it is possible to pick 8 green and 5 red balls (13 total) without picking any white ball.
- (d) 11
- 11 is insufficient because it is possible to pick 8 green and 3 white balls (11 total) without picking any red ball.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.