UPSC Prelims 2005 · General Studies
Question 119: Basic Numeracy
Ten identical particles are moving randomly inside a closed box. What is the probability that at any given point of time all ten particles will be lying in the same half of the box?
AnswerThe answer is (d).
Each particle is in either half independently with probability 1/2. All ten in one particular half has probability (1/2)^10 = 1/1024; either half can be the one, so double it: 2/1024 = 1/512. In general, for n particles the chance that all lie in one half is 2 × (1/2)^n, which falls very fast as n grows.
Why each option is right or wrong
- (a) 1/2 ignores that all ten must be together.
- (b) 1/5 has no basis here.
- (c) 2/11 has no basis here.
- (d) Correct: 2 × (1/2)^10 = 1/512.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2005, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.