A large laboratory runs 10,000 SSTs daily through the Chemistry
analyzer and 4500 Hepatitis B surface Antigen tests through their
Immunology analyzer every day. The lab manager worries about
reporting a false positive HBsAg result because the Chemistry
analyzer
doesn't use discrete tips when sampling. The Chemistry Supervisor
doesn't want to seperately aliquot the sample becaise of the risk of
potential mislabling and possilbe aeresol contamination, which also
could result in a false positive. So he assures his manager that
sharing the tube between instruments is not likely to ever result in
reporting a false positive HBsAg.

- A phlebotomist draws two SSTs and three other tubes from a patient
with hepatitis (Patient A). The blood is taken to the laboratory
for testing.
- The primary SST is placed on a Chemistry instrument that uses
washes
between each test and has a 1 in 10 chance of contaminating the
subsequent tube.
- Any SST sample following Patient A's hepatitis positive SST has a
25% chance of having a hepatitis test ordered.
- In order to be deemed positive, a patients sample must be repeated
using an alternate tube if available, and if the repeat is found to
be
positive, it then has to be confirmed using an alternative method and
an alternative sample.
- 99% of the patient samples that have hepatitis ordered have at
least
3 different tubes drawn that can be used for repeat and confirmation.
- Of the remaining 2%, 1% go one the Chemistry analyzer and could
possilbly be contaminated by Patient A's sample, the other 1% go
directly to the hapatitis analyzer for testing.


What is the probability of reporting a false positive result?