# Probability for N molecules

1. Nov 8, 2013

### curiousKevo

Estimate the probability that in a room of volume V, all the N molecules of air are found in volume $\frac{3V}{4}$ and none at all in the reaining volume V/4
My take to the solution is

Pr of finding N molecules in $\frac{3V}{4}$ : $\frac{N}{3V/4}$= $\frac{4N}{3V}$
Pr finding none in V/4: 1-$\frac{4N}{3V}$ = $\frac{3V-4N}{3V}$

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I used coin toss logic. No idea i did it correct. I'm new at staistical mechanics. I'm kinda lost just give me hints.

Last edited: Nov 8, 2013
2. Nov 8, 2013

### stevendaryl

Staff Emeritus
That's not a very good estimate. Think about it this way: You divide the room into two parts, call them section A and section B. Section A is 3 times as large in volume as section B.

Suppose you start off with an empty room (no air at all). Then you introduce a single molecule into the room at a random location. Then the probability will be 3/4 that the molecule will be placed into section A. Now introduce a second molecule. The probability that it will be in section A is again 3/4. So the probability that the first two molecules will be released into section A is:

$P_2 = (3/4)*(3/4) = (3/4)^2$

So if you keep on releasing molecules into the room at a random location, then the probability that the first $N$ molecules will all be in section A is:

$P_N = ?$

3. Nov 8, 2013

### curiousKevo

Thx!

Last edited: Nov 9, 2013