Apparent paradox in Geometric probability problemSuppose we have N particles in a box. We can consider these particles to be distinguishable, and move about the box randomly, like molecules of gas in a box. Suppose, the volume of this box is V.I've been asked to find the probability that at a certain time, a small sub-volume V 0 does not have a single particle inside it.

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Apparent paradox in Geometric probability problemSuppose we have N particles in a box. We can consider these particles to be distinguishable, and move about the box randomly, like molecules of gas in a box. Suppose, the volume of this box is V.I&#039;ve been asked to find the probability that at a certain time, a small sub-volume       V    0   does not have a single particle inside it.

snowman8842 · Accepted Answer

Step 1The probability of a single particle being in region       V    0  , is simply             V      0        V  .Hence the probability of a single particle, not being in the region is simply   1  −  (            V      0        V    )Step 2Hence, the probability that N particles are not in that region would be given by:  P  =  [  1  −  (            V      0        V    )      ]    N

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