확률

P(A) = n(A) / n(S)

The simplest truth: probability is the ratio of favorable outcomes to all possible outcomes. A fraction that contains the universe.

P(A|B) = P(B|A) · P(A) / P(B)

Bayes' theorem: how the observation of evidence updates our belief. The mathematical expression of learning from experience.

E[X] = Σ x_i · P(x_i)

Expected value: the center of gravity of chance. Where all possible outcomes, weighted by their likelihood, converge into one number.

σ² = E[(X - μ)²]

Variance: the measure of uncertainty itself. How widely the possible scatters from the expected. The mathematics of doubt.

lim_n→∞ S_n/n = μ

The Law of Large Numbers: given enough attempts, the average converges to the expected. Patience reveals the true nature of chance.