Bayes' Theorem

= ·

Tap a term to see what it means, or .

Calculate

Example: a disease affects 1% of the population. A test detects 95% of sick people, but also comes back positive for 5% of healthy ones. If your test is positive, what is the chance you have the disease? Here A is “having the disease” and B is “testing positive”. Change the values to work out your own case.

Prior P(A) (%) Likelihood P(B|A) (%) False positive P(B|¬A) (%)

Step by step

What each term means

Posterior: The probability of A given that B happened. It updates the belief about A after observing B.
Likelihood: The probability of observing B if A is true. It says how compatible A is with the data B.
Prior: The initial belief about A before observing B. It may come from previous knowledge or assumptions.
Marginal (Evidence): The probability of observing B across all scenarios; it normalizes the equation. Computed with the law of total probability: P(B) = P(B|A) · P(A) + P(B|¬A) · P(¬A)