Conditional Probability
Conditional probability is the probability of an event given that another event or condition is true, often written as P(A given B).
Definition
Conditional probability describes probability under a condition. It is commonly written as P(A given B), meaning the probability of A assuming B is true.
Why it matters
Conditional probability is the language of evidence. In Bayes updates, you compare how likely evidence is under different hypotheses, which leads to a likelihood ratio and an updated posterior probability.
How it connects
• Conditional probability connects to likelihood and Bayes theorem.
• In diagnostic style inputs, sensitivity and specificity are conditional probabilities.
Common pitfalls
Confusing directions: P(A given B) is not the same as P(B given A).
Forgetting base rates: Conditional evidence does not replace the base rate.