3 ms·
It's the same reason that the first test doesn't get you 1%, but the testing pool has changed. Instead of testing 10000 people without and 1 person with, you're
by andreareina 5y ago
It's the same reason that the first test doesn't get you 1%, but the testing pool has changed. Instead of testing 10000 people without and 1 person with, you're testing 100 people without (and the same person with).
It's a Bayesian update. Every (independent) positive result increases your confidence of having the condition by 100x. At first you have no information so you assume the base rate, 1:10000. At the first test, that goes to 100:10000. Second test gets you to 10000:10000 or even odds. Third positive result finally gets you to 1000000:10000, or a 99% confidence of having the condition.