UPSC Prelims 2000 · General Studies
Question 142: Basic Numeracy
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 blind-folded (without replacing any of it) to be assured of picking at least one ball of each colour?
AnswerThe answer is (d).
Think of the worst case. You could pick all 8 green and all 7 white balls, 15 in all, and still have no red ball. The 16th ball must then be red, so 16 balls guarantee at least one of each colour. For a guarantee you must allow for the worst order of draws, not the likely one.
Why each option is right or wrong
- (a) 4 balls could all be green.
- (b) 7 balls could all be green or white.
- (c) 11 balls could still be 8 green and 3 white.
- (d) Right: after 15 balls the 16th must be red.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2000, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.