Bayes Theorem Calculator — 公式
## How to Apply Bayes' Theorem
### Formula
**P(A|B) = P(B|A) * P(A) / P(B)**
where P(B) = P(B|A)*P(A) + P(B|not A)*P(not A)
Bayes' theorem updates a prior belief P(A) after observing evidence B. The likelihood P(B|A) measures how probable the evidence is if A is true. The denominator P(B) normalizes the result.
### Formula
**P(A|B) = P(B|A) * P(A) / P(B)**
where P(B) = P(B|A)*P(A) + P(B|not A)*P(not A)
Bayes' theorem updates a prior belief P(A) after observing evidence B. The likelihood P(B|A) measures how probable the evidence is if A is true. The denominator P(B) normalizes the result.
计算示例
A disease affects 1% of the population. A test is 90% sensitive and has a 5% false positive rate. If someone tests positive, what is the probability they have the disease?
- P(A) = 0.01 (prior: disease prevalence)
- P(B|A) = 0.9 (sensitivity)
- P(B|not A) = 0.05 (false positive rate)
- P(B) = 0.9 * 0.01 + 0.05 * 0.99 = 0.009 + 0.0495 = 0.0585
- P(A|B) = (0.9 * 0.01) / 0.0585 = 0.009 / 0.0585 ≈ 0.1538
- Despite a positive test, there is only about a 15.4% chance of having the disease.