A diagnostic test for the presence of HIV has the following characteristics: when a person who is actually not infected with the virus is tested, the test has probability 0.005 of indicating that the virus is present.

140 employees of a medical clinic, who are all actually free of the virus, are tested. Assume that the 140 people are independent. Let X = # of employees, out of the 140, who test positive.

a) What is the probability distribution of X? (All you have to do here is write "X ~ " and then fill in what comesnext -and, of course, you have to justify this answer).

b) Find Pr(X > 0).