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 properties of the test: this isn’t enough information for an answer.

If the test is failing for reasons that are independent from one test to another (say, there was a manufacturing defect in one test), then you’d have independent probabilities of failure, and the chance would be (1-0.98)(1-0.98) = ~0.04% of both being wrong (i.e., about 2% of 2%).

But if they’re wrong for some underlying reason (say, you aren’t exposing the specific antigen it’s testing for), then one failing would ensure the other fails, and it’d still be 2%.

More likely, both failure modes are possible, and the probability is somewhere between these extremes.