What we have here is:

* 1% are infected

* 99% are NOT infected

We have to find two probabilities here:

(1) an infected person test shows positive result (correct result): (Let A)

It's 95% of 1% so, P(A) = 0.95 * 0.01 = 0.0095

(2) a person who is not infected shows a negative (correct) result in the test: (Let B)

It's 98% of 99% so, P(B) = 0.98 * 0.99 = 0.9702

So success rate would be P(A) + P(B) = 0.9702 + 0.0095 = 0.9797