Question

Consider that you have an opaque box with two identical compartments (A, B). Within the box has 4 red balls and 4 blue balls

a ) How many possible microstates does your system have?

b ) What is the entropy of the system?

Answer #1

Suppose three red and one blue marbles are placed inside a
container that is opaque (you can’t see into the container). If two
marbles are selected at random without replacement answer the
following questions:
a) How many possible samples of size 2 can you create?
b) List the set of all possible outcomes here (a tree structured
diagram might prove helpful here):
c) List the outcomes that make up the following event: “a red
and a blue marble are selected”....

There are ? colored balls in a box. The number of red balls is
??, the number of green balls is ?? and the number of blue balls is
?? (?=??+??+??). We want to arrange all the balls in a row. We do
it in 3 steps. First, we arrange the red balls, then we arrange the
green balls and then we arrange the blue balls.
a) How many possible arrangements are there for the red balls in
the first...

Suppose you have a box with 10 red balls, 4 green balls, and 6
blue balls. Answer the following questions. Think about the
questions below. They look similar, but how are they different?
a) You randomly select two balls from the box. What is the
probability of selecting two red balls?
b) Suppose you are asked to draw a ball, return whatever you
picked, and draw another ball. This is called sampling with
replacement. What is the probability of selecting...

We have 6 atoms in a box and we place a divider in it at a
random time. What are the possible macrostates of the atoms? How
many microstates exist at each macrostate? Determine the entropy
for each macrostate.

1. I have a pile of n identical ping-pong balls and two boxes,
labelled Box 1 and Box 2. How many different ways are there to
distribute the n balls into the two boxes? Explain why your answer
is correct.
2. How many ways are there to distribute n ping-pong balls among
k boxes?
3. I have n books with n different titles. I want to put them on
shelves in my library. How many different ways are there to...

A large rectangular vessel is divided by a partition into two
compartments of identical shape, size, and temperature. One mole of
fluorine gas is placed in the left compartment and one mole of
nitrogen gas is placed in the right compartment. You may assume
that both gases behave ideally.
(a) Which compartment has the greater
pressure?
The left compartment has the greater pressure.
The right compartment has the greater
pressure.
Both compartments have the same pressure.
(b) Which compartment has...

i need to have this done soon. Thank You! :)
There are four different boxes labeled A, B, C and D. Box A has
3 red , 4 blue and 2 green balls. Box B has 3 red , 5 blue and 6
green balls. Box C has 4 red , 6 blue and 8 green balls. Box D has
5 red , 6 blue and 7 green balls. If one box is selected at random
and a ball is...

This question is about
the Bayes' Theorem.
You are given two
boxes. Box 1 contains 5 red, 5 green, and 3 blue balls, and Box 2
contains 4 red, 3 green, and 2 yellow balls. You are asked to
randomly pick one of the two boxes. Holding that box, you grab one
ball at random, and then set the box back down. You found out that
it is a red ball. Let A be the event that you choose Box...

There is a box with two colored balls, red balls and blue balls.
The probability of selecting a red ball is 10%. The balls are
independent of each other, and after each trial of choosing a ball,
you put it back in the box.
1.) What is the probability your first red ball that you get
will be on your 3rd or 5th trial?
2.) What is the probability your first red ball will be on an
even trial? (Trial...

A system of 6 identical 1-dimensional harmonic oscillators (it
could be two atoms of an Einstein model solid). What is the
probability that the first oscillator has 2 quanta of vibrational
energy when the system has 3 quanta of vibrational energy?
Hint: You may find it useful to consider how many microstates
the system has and how many microstates the rest of the system has
when the first oscillator has 2 quanta.
Answer is 5/56
For the system considered in...

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