Asystem has three macrostates. macrostates 1 and 3 are least likely and have one basic state each. macrostate 2 is the equilibrium state and is four times more likely to occur than either of the other two macrostates.
part a
what is the probability that the equilibrium state 2 occurs?
express your answer using three significant digits.
p2=
part b
what is the probability that macrostate 1 occurs?
express your answer using three significant digits.
p1=
part c
what is the probability that macrostate 3 occurs?
express your answer using three significant digits.
p3=
part d
what is the sum of the probabilities for all macrostates?
express your answer using three significant digits.
p=

Explanation:

Let's start writing the sample space for this exercise :

Let be ''M'' an abbreviation for Macrostate

Ω = { M1 , M2 , M3 }

Let be P(M1) the probability of Macrostate 1.

Reading the exercise, we know that ⇒

Let's note this probability as ''p''.

Macrostate 2 is four times more likely to occur than either of the other two macrostates ⇒

The sum of all probabilities must be equal to 1 for this sample space.Therefore,

Finally :

For Part A :

For Part B and C :

For Part D :

The sum of the probabilities for all macrostates is equal to 1 :

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

f=ma a/f/m a= 480/60 a = 8m/s/s that is quick wow