Answer to Question #110621 in Classical Mechanics for Tanya Saini

Question

Q.Consider an isolated system of ten particles undergoing random collisions, and confined
to a cubical box of volume V. Compare the probabilities that all the particles are in the left
half vs five particles are in the left half. Is this in contradiction with the principle of equal
a-priori probabilities.

Answer 1

As per the given question,

total number of particle = 10

there is two partition of the volume.

So the probability of the particle be in half = 1/2

now as per the probability distribution function,

probability of the particle 5 particle left side $=\dfrac{1}{2^5}$

similarly, probability of the 10 particle to be left side =$\dfrac{1}{2^{10}}$

Hence the required ratio = $2^5$