Bayes Theorem Calculator

Bayes' Theorem Formula

P(A|B) = P(B|A) × P(A) / [P(B|A) × P(A) + P(B|¬A) × P(¬A)]

Where:

• P(A|B) = Posterior probability - the probability of A given B
• P(B|A) = Likelihood - the probability of B given A
• P(A) = Prior probability - the probability of A before considering B
• P(¬A) = The probability of not A (1 - P(A))
• P(B|¬A) = False positive rate - the probability of B given not A

In Medical Context:

• P(Disease|Positive) = P(Positive|Disease) × P(Disease) / [P(Positive|Disease) × P(Disease) + P(Positive|No Disease) × P(No Disease)]
• P(Disease|Positive) = Sensitivity × Prevalence / [Sensitivity × Prevalence + (1 - Specificity) × (1 - Prevalence)]