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A cube that has a volume of 1.00 m³ contains N distinguishable particles.
1. Determine the probability that all the particles are in a smaller volume V of the cube if N = 1 and V = 0.500 m³.
2. Determine the probability that all the particles are in a smaller volume V of the cube if N = 1 and V = 0.300m³.
3. Determine the probability that all the particles are in a smaller volume V of the cube if N = 1 and V = 0.0100³.

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Answer:

1 P = 0.5

2 P = 0.3

3 P = 0.01

Explanation:

The probability formula is

          [tex]P =V^N[/tex]

Where P is the probability  V is the volume while N is the number of distinguishing particles

So for N = 1 and [tex]V = 0.500m^3[/tex]

           [tex]P = (0.500m^3)^1\\[/tex]

               = 0.5

For  N = 1 and [tex]V = 0.300m^3[/tex]

           [tex]P = (0.300m^3)^1[/tex]

               = 0.3

For   N = 1 and [tex]V = 0.0100m^3[/tex]

     [tex]P =(0.0100m^3)^1[/tex]

         = 0.01

         

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