Lab tests aren't perfect. There will always be false positives and false negatives.
Getting the test right and using it in the right people is so important.
I used to be a Clinical Biochemist (a long time ago) until life got in the way.
The key words are specificity and sensitivity.
Sensitivity - say it is 99%. That means that if 100 people have the disease, 99 of them would test positive
Specificity - say it is 99%. That means that if 100 people did not have the disease, then 99 of them would test negative.
This is really important when you screen people.
Imagine 10% of the population you screen have the antibody - so they have been exposed.
10,000 people tested. 1000 have the antibody, 9000 don't.
People with the antibody - 99% sensitive
990 positive (true positive)
10 negative (false negative)
People with no antibody
99% specificity
9801 negative (true negative)
99 positive (false positive)
So out of 1089 positive tests, 990 are actually positive.
So if you have a postive test, you have a 90% chance of having antibodies.
That's assuming 10% of the population have had the disease and the test has 99% sensitity and specificity