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Probability: Diseases in Military

Only answer parts C) and D) of the attached question, please.

Each of 500 soldiers in an army company independently has a certain disease with probability 1/10[cubed]. This disease will show up in a blood test, and to facilitate matters blood samples from all 500 are pooled and tested.
One of the 500 people is Jones, who knows that he has the disease.
C) What does Jones think is the probability that more than one person has the disease? As the pooled test was positive, the authorities have decided to test each individial seperately. The first i - 1 of these tests were negative, and the i-th one - which was Jones - was positive
D) Given the prededing, as a function of i, what is the probability that any of the remaining people have the disease.

The problems are from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions.