Here are to challenge questions given to the class to answer to be turned for a free slice of pizza. We have to days, and he said we can get help, and I'm taking him at his word. Here they are. 1). Suppose a room is divided into the front fifth, the middle fifths, and the back two fifths. What is the ratio of the probabilities of finding a 20%:40%:40% split in the particles (the most likely distribution), as opposed to a 19.9%:40.2%:39.9% split.( Assume all the particles are identical. . (Leave answer in terms of N, the total number of particles. But recognize that N is a large number) 2). Consider the case of a gas in the atmosphere. Assume that the temperature is constant. Basd on the maxwell Boltzman distribution, at sea level the atmosphere contains 78.1% N2m 21% O2, 0.9% argon and 0.036 CO2. What are the ratios at the top of Everest? relevant equations Boltzmann-Maxwell. 3. The attempt at a solution For The first one. Probability of finding a 20%:40%:40% split: 1 Probability of finding a 19.9%:40.2%:39.9% split= 19.9/20*39.9/40= 0.9925125 For the second, I don't even know where to begin. I know the probability is supposed to be lower (right?), but that is about it. I know we're still going to get the pizza, but this bothering me to no end. I have to know it, and this why I joined, and will hopefully contribute in turn.