Calculate propability of certain outcome

[lotw]

So I have a question, these statistics lessons have been such a long time that I'm not sure how to calculate the following:

Say that there is a new disease, and I have a test that is 100% reliable. I have tested 100 people, and have found that 3 people got the disease.
So from now on this is the assumption: there is a 3% change of having (and finding) that a person has the disease.

Now I , say I would like to test 10 people. How do I calculate that by chance, none of these people have the disease. Would it be a calculculated by just (0.98)^10 =0.817?

I feel that this isn't right, as I just adjust the chance of finding the disease over how many people are left to test. So I guess I should adjust the chance of not finding the disease (98%) after each person testes negative..? But I'm not sure how to do this.. Could someone help me?

 

[Archidamus]

First lets address the testing of 100 people and finding that 3 have it. 3% is your estimated prevalence of the disease, not the true prevalence. You would need to test everyone, or a massive amount of people, to come up with an accurate population prevalence.

Next, using this estimated prevalence of 3%, you can estimate the probability that zero out of 10 people have it by (1-.03)^(10) = .97^10 = 73.74%