eli5: how does the probability of something being wrong (e.g., a false negative on an at-home/rapid antigen test) change when you do the same test multiple times?

Question

if there is a 98% chance the results will be correct (making it ~1/50 times it will be incorrect), would taking the test twice make the chance of it being incorrect ~1/100? then after three times ~1/200? or would it not change at all and still be 1/50?

In: 0

Answer 1

It depends on the desired outcome (confirmation bias). You believe you’re sick, you take a test which has 95% of giving you ring result and your healthy. You take it twice and you have 10% chance that one of them will show you’re sick. If you believe you’re healthy, then it’s enough for one test to show you’re not sick, so chance is 99.75% because you pick the suitable result.