tools

    Bayes calculator

    Update a probability with new evidence using Bayes’ theorem.

    Enter as
    Second likelihood
    %

    Test 1

    %
    %
    Result
    P(H|E)8.33%

    P(H|E) = P(E|H) × P(H) ÷ [P(E|H) × P(H) + P(E|¬H) × P(¬H)] = 90% × 1% ÷ (90% × 1% + 10% × 99%) = 8.33%

    Posterior odds = prior odds × likelihood ratio = (1 : 99) × 9 = 1 : 11

    Posterior P(H|E)
    8.33%
    Posterior P(H|¬E)
    0.11%
    Chance of a positive P(E)
    10.8%
    Positive likelihood ratio
    9
    Negative likelihood ratio
    0.11
    Prior odds
    1 : 99
    Posterior odds
    1 : 11

    Out of 1,000 people, 10 have H and 990 do not. 9 of the 10 with H test positive, and 99 of the 990 without H also test positive.

    So 9 of the 108 positives (8.33%) have H. Of the 892 negatives, 1 (0.11%) have H.

    • H, positive: 9 people
    • H, negative: 1 person
    • Not H, positive: 99 people
    • Not H, negative: 891 people