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o 4/29/2016 10:55 PM 0 87.4/1004/14/2016 04:41 PM Gradebook PrintCalculatorPeriodic Table Print Calculator Question 20 of 21 Incorrect Map sapling learning A certain box contains 200 particles of an ideal gas. How many times more likely is it to find the particles evenly split between the left and right halves of the box, than to find 160 particles on one side and 40 on the other? Number 2.2 x 1016 Previous 8 Give Up & View Solution e Check Answer Next Exit 8 Hint Find the multiplicity for each of the two configurations. Since each of N particles can only be in one of two sides, the total number of possible configurations is 2NExplanation / Answer
Each particle has two possibilities: either it is on the left hand side or it is on the right hand side
probability
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
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