Free entry
Card Odds
Estimate the chance of a card event. Compete on the accuracy of your probability judgment.
MO STATS · FREE CALCULATOR
Bayes’ Theorem Calculator
Specify the prior probability and how likely the same evidence is under each of two hypotheses.
No account to calculateNo real-money wageringTransparent assumptions
CALCULATOR
Bayes calculator
Update the probability of a hypothesis after observing a positive signal.
Start with your assumptions
Enter values and calculate to see the result, method, and assumptions.
PUT YOUR JUDGMENT TO WORK
Compete on decisions.
Free entry
Bankroll Arena
Choose a stake for a simulated opportunity. Compete on the quality of the decision under stated odds.
Games award nonredeemable MO Chips and decision scores. Chips cannot be bought, transferred or exchanged, and game results never earn anything of monetary value. Subscribing gives no competitive advantage.
Worked example
- Probability of evidence
- 17.0000%
- Posterior probability
- 47.0588%
Suppose a condition has prior probability 10%. Evidence appears with probability 80% when the condition is true and 10% when it is false. Out of 1,000 modeled cases, 80 true cases and 90 false cases show the evidence. The posterior is 80 ÷ 170 = 47.0588%.
Example inputs
- prior:
0.1 - likelihoodIfTrue:
0.8 - likelihoodIfFalse:
0.1
Method
P(H | E) = P(E | H)P(H) ÷ [P(E | H)P(H) + P(E | not H)(1 − P(H))]. Both likelihood inputs must describe the same observed evidence. The two hypotheses must be mutually exclusive and exhaustive.
Assumptions
A posterior depends on the prior and likelihood model. Repeating an update with the same dependent evidence can overstate confidence. If the supplied evidence has zero probability under both hypotheses, the posterior is undefined and the tool returns an input error.
Related
Create a free MO Stats account to save your work and join competitions.