Consider a series of 8 flips of a fair coin a Calculate the

Consider a series of 8 flips of a fair coin.

(a) Calculate the probabilities for obtaining 0-8 heads. We will consider each of these nine outcomes to be macrostates of the system.

(b) Calculate the entropy for each of these macrostates.

I was able to find the probibiliteis for each, but am stuck with entropy.

Solution

a)

Probability will be a binomial distribution

for x=0 heads

P(X=0)= 8C0 * 0.5^0 * 0.5^8-0

P(X=1)= 8C1 * 0.5^1 * 0.5^8-1

and so on...

b) entropy is something of physiscs you should post it in physiscs