Consider this:
If a test gives a positive result for an infected person 98% of the time, that means that 2% of the time, it gives a negative result for an infected person, which would be a false negative.
Then,
if the test is 97& accurate (not precise) for non-infected people, that means that it gives a negative result 97& of the time. So a positive result will be given 3% of the time for non-infected people, which is considered a false positive.