Updating Beliefs

Discrete Math · Axiom Academy

Experience how new information changes what we believe. See probability in action through medical diagnosis! A patient comes to the clinic with symptoms. Before any tests, what's the probability they have Disease X? The doctor orders a blood test. This test is 80% accurate at detecting Disease X when present. Let's see the result! To be more certain, the doctor orders an imaging scan. This test is 90% accurate when Disease X is present. What will happen to our probability now? Let's explore an alternate scenario. What if the second test came back negative instead? Different diseases have different base rates. Choose a disease and see how test results update the probability differently! The Mathematics of Updating Beliefs You experienced conditional probability in action! Every time new information arrives (a test result), we update our belief about the probability. This isn't guesswork – there's a precise mathematical formula for how to update. The mathematical rule you witnessed is called Bayes' Theorem . It tells us exactly how to combine our prior belief (base rate) with new evidence (test results) to get an updated probability. It's used everywhere: medical diagnosis, spam filters, machine learning, and scientific research!

This is the written version of the interactive lesson above. See the full Discrete Math course.