Bayesian Updating

a belief about a coin, revised by evidence

Plate XIII
Heads / Tails0 / 0
Posterior mean0.500
PosteriorBeta(1, 1)
True bias0.70

Start from a flat prior over the coin’s bias $p$. Each flip multiplies by the likelihood; the posterior $\mathrm{Beta}(1{+}H,\,1{+}T)$ sharpens toward the truth. After T. Bayes, 1763 · P.-S. Laplace