Bayes’ rule updates a prior by comparing all ways the observed evidence can occur.
WHAT HAPPENS IF…With p=0.01, sensitivity 0.99, and false-positive rate 0.05, what is the posterior?
Interactive exploration
Loading the mathematical model…
Connect the picture to the ideaP(A∣+)=P(A)P(+∣A)+P(Ac)P(+∣Ac)P(A)P(+∣A)
The numerator is the joint true-positive mass ps. The denominator adds false positives from the complementary group, (1−p)f. Dividing rescales the positive subset to total mass one. If that subset has probability zero, the displayed conditional probability is undefined.
A detail that matters
A high true-positive rate does not imply the same posterior probability; the base rate matters.