Bayes Probability calculator

You have (a belief about) a hypothesis. See some evidence about it. How should this information update your prior belief.

Instead of using the meaningless A and B, we use here H for hypothesis and E for evidence.

P(H) the probability of the hypothesis being true before any evidence. The current belief about the hypothesis; the "prior".
P(E|H) the probability of seeing evidence if the hypothesis is true. The "likelihood".
P(E) the probability of seeing evidence.
P(H|E) the probability the hypothesis is true given some evidence, i.e. when E is true. The new, updated belief about the hypothesis; the "posterior".

Bayes' formula:
P(H|E) = P(H)·P(E|H) / P(E)              P(E)=P(H)·P(E|H)+P(H̄)·P(E|H̄)

How often the hypothesis is true among the cases where the evidence is true , i.e. what proportion.

Enter these 3 probabilities. OR    Enter these 4 data counts.
P(H):     P(H̄)= H H̄
P(E|H): P(H)P(E|H)= EH EH̄
P(E|H̄): OR P(E): P(H̄)P(E|H̄)=

P(H|E)=       = /(+)

Area=1 i.e. all possibilities.

P(E)=P(H)P(E|H)+P(H̄)P(E|H̄) = total probability of seeing the evidence.
P(H|E) = P(H)P(E|H) / (P(H)P(E|H)+P(H̄)P(E|H̄)) = the proportion of the possibilities fitting the evidence that supports the hypothesis.