Testing Positive

Conditional probability and Bayes

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $P(A \mid B)$ is the probability of $A$ when you know $B$ happened. It is not the same as $P(B \mid A)$.
• For rare conditions, even accurate tests give many false positives. Always consider the base rate.
• Bayes’ theorem updates probabilities as evidence arrives.

Steps

1. Given that…
2. The test
3. Count real people
4. A common disease
5. Bayes’ theorem
6. Fewer false alarms
7. Test again