Basic Probability Notation: Bayes' Rule

Bayes' Rule permits us to reverse the direction of a conditional probability. This is especially useful in diagnosis applications (medicine, engineering, etc.) when we know the probability that a given condition causes a given symptom, and we see that symptom. We need to know the probability that the condition is true.

P(B|A) = P(A|B)P(B)/P(A).

P(Y|X,E) = P(X|Y,E)P(Y|E)/P(X|E).

• Meningitis causes a stiff neck 50% of the time.

• The unconditional prob of having meningitis is 1/50,000.

• The prior prob of having a stiff neck is 1/20.

• What is the probability that a patient has meningitis given that the patient has a stiff neck?