A coin with a hidden probability p. Start from a prior and watch the posterior sharpen with every observation.
PosteriorPrior95% CI
Observation history
You haven't flipped the coin yet.
Prior Beta(α₀, β₀)
Your belief before any data. Larger values = stronger prior conviction.
Posterior summary
Observed (H / T)
0 / 0
Estimate p̂ (posterior mean)
0.500
Mode (MAP)
not unique
Uncertainty σ
0.289
95% credible interval
[0.02, 0.97]
Your guess for p
Guess: 0.50
How Bayesian updating worksThe coin's true probability p is unknown. Start from a prior Beta(α₀, β₀); every heads adds 1 to α and every tails adds 1 to β to give the posterior (Beta-Binomial conjugacy). The more you observe, the sharper the peak and the closer it sits to the true p.Posterior = Beta(α₀ + heads, β₀ + tails)