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ch4aika [34]
2 years ago
14

A certain box contains 200 particles of an ideal gas. how many times more likely is it to find the particles evenly split betwee

n the left and right halves of the box, than to find 160 particles on one side and 40 on the other?
Chemistry
1 answer:
Strike441 [17]2 years ago
5 0

 Each particle has two possibilities: either it is on the left hand side or it is on the right hand side.  

The probability of having them equally split is  

P(100,100) = 200C100 / 2^200  

where 200C100 is the binomial coefficient.  

For the uneven distribution we have  

P= 2 * 200C160 / 2^200  

where the factor 2 comes in because we could have 160/40 or 40/160 as a division.  

So the ratio of probabilities is  

200C100 /(2 * 200C160 )  

= 2.2 * 10^16

Hope this helps!

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