Question map
Not attempted Correct Incorrect ★ Bookmarked
Loading

Q4 (IAS/2005) Science & Technology â€ș Basic Science (Physics, Chemistry, Biology) â€ș Quantitative aptitude topics Answer Verified

Ten identical particles are moving randomly inside a closed box. What is the probability that at any given point of time all the ten particles will be lying in the same half of the box ?

Result
Your answer: —  Â·  Correct: D
Explanation

The answer depends on how the sample space is counted. If the ten particles are treated as indistinguishable and only the occupancy numbers of the two halves matter (a Bose-like counting where swapping particles does not generate new microstates), the possible occupancies of one half are 0,1,2,...,10 — eleven equally possible outcomes — and the two favorable outcomes are 0 or 10, giving probability 2/11 [1]. By contrast, treating particles as distinguishable (independent placements) yields probability 2·(1/2)^10 = 1/512, but that uses a different microstate counting assumption. The question’s phrasing (“identical particles”) points to the indistinguishable counting and hence 2/11.

Sources

  1. [1] https://courses.physics.illinois.edu/phys213/sp2013/lectures/lecture7.pdf
How others answered
Each bar shows the % of students who chose that option. Green bar = correct answer, blue outline = your choice.
Community Performance
Out of everyone who attempted this question.
50%
got it right
✓ Thank you! We'll review this.

SIMILAR QUESTIONS

IAS · 2006 · Q94 Relevance score: -5.65

3 digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that their product is odd?

IAS · 2004 · Q147 Relevance score: -5.94

Three students are picked at random from a school having a total of 1000 students. The probability that these three students will have identical data and month of their birth is:

CAPF · 2012 · Q87 Relevance score: -6.12

10 identical coins are lying on a table having head H face as the upper face. In one attempt, exactly four coins can be turned upside down. What is the minimum total number of attempts in which tail T face of all the 10 coins can be brought to be the upper face?

CDS-II · 2018 · Q7 Relevance score: -6.25

A particle moves with uniform acceleration along a straight line from rest. The percentage increase in displacement during sixth second compared to that in fifth second is about

NDA-I · 2008 · Q13 Relevance score: -6.39

The neutron, proton, electron and alpha particle are moving with equal kinetic energies. How can the particles be arranged in the increasing order of their velocities?