N statistically independent particles are contained in a box

N statistically independent particles are contained in a box of volume V = L times L times L. We denote nL and nR (nL + nR = N) as the number of particles in the left and right parts of the box of the volumes VL and VR. respectively. Take: V = VL + VR Derive probability P(n) to find nL = ^ + n particles if VL = VR. Take N = 100 and n = 5. Find P(n) if VL = 2VR.

Solution

VL = Vr means V= 2Vr

b) P(n) = 55/100 =0.55

c) If Vl = 2Vr then V = 3Vr

50/2+n/50 = (n+25)/50

P(n) = (n+25)/100