91影视

(a)We suppose we flip 20 coins, $n=20$. The total number of microstates will be:

Calculation method

$2^n=2^{20}$

$=1048576$microstate

So, the answer is $2^{20}$or 1048576 microstates.

(b)The likelihood of obtaining any specific sequence of heads and tails (for example HTHHTTTHTHHHTHHHHTHT) is

$P=\frac{\text{Favorable microstate}}{\text{Total number of microstates}}$

$\begin{array}{r}=\frac{1}{2^n}\\ =\frac{1}{2^{20}}\end{array}$

$=\frac{1}{1048576}$

$=9.536脳{10}^{鈭�7}$

As a result, the answer is for the sequence of heads and tails. (for example HTHHTTTHTHHHTHHHHTHT) is $\frac{1}{2^{20}}$or $9.536脳{10}^{-7}$.

(c)Regardless of order, the probability of getting the macrostate of 12 heads and 8 tails is given by:

$P=\frac{\left(\begin{array}{l}N\\ n\end{array}\right)}{\text{Total number of microstates}}$

where n denotes the number of heads and N denotes the number of coins, so:

$P=\frac{\left(\begin{array}{l}20\\ 12\end{array}\right)}{1048576}$

After arranging we get,

Finally solution is

$P=\frac{125970}{1048576}=0.12$