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Important information about Basic Probability

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.

a) What is the (approximate) probability that the blood test will be positive (and so at least one person has the disease)? Suppose that the blood test yields a positive result.

b) What is the probability under this circumstance, that more than one person has the disease? One of the 500 people is Jones, who knows he has the disease.

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