Microstate Selection Probability Cross-Scan - Statistical Physics: Ensembles, Weights, and Fluctuations Step by Step

Three counted buckets show probability as selected count over the same total. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Bucket row 1 uses count over total

Bucket 0 has selected count 1 out of total 4, so the probability is 1/4.

P(\hbox{bucket }0)=\frac{1}{4}=\frac{1}{4}

Bucket row 2 uses count over total

Bucket 1 has selected count 2 out of total 4, so the probability is 1/2.

P(\hbox{bucket }1)=\frac{2}{4}=\frac{1}{2}

Bucket row 3 uses count over total

Bucket 2 has selected count 1 out of total 4, so the probability is 1/4.

P(\hbox{bucket }2)=\frac{1}{4}=\frac{1}{4}

Probability follows selected count over the same total

The total stays four. Counts one, two, and one give probabilities one fourth, one half, and one fourth.

\begin{array}{c|c|c|c}bucket&count&\Omega&P\\0&1&4&\frac{1}{4}\\1&2&4&\frac{1}{2}\\2&1&4&\frac{1}{4}\\\end{array}