A Baye's Theorem Question

A Drug testing laboratory produces false-negative results 2% of the
time, and false-positive results 5%, of the time. The laboratory tests
a company in which 10% of the employees use drugs.

a) What is the probability that a non-drug user will test positive for
drug use twice in a row.
b) What is the probability that someone who tests positive twice in a
row is not a drug user.

Drug-user = D, Non-Drug user = ND, Positive = Pos., Negative = Neg

Pr(D) = 0.10, Pr(ND), = 0.9, Pr(Pos|ND) = 0.05, Pr(Pos|D) = 0.98,
Pr(Neg|ND) = 0.95
Pr(Neg|D) = 0.02

a) So if E = {non-drug-user tests pos}, and F={non-drug-user tests
pos}, which should be independent events then Pr(E and F) = E(F) =
..0025. I'm not too sure about this answer.

any help would be much appreciated.

.

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