Question

Stats Problem Help please
Using Composite Blood Samples
When doing blood testing for HIV infections, the
procedure can be made more efficient and less expensive by combining samples of
blood specimens. If samples from three people are combined and the mixture tests
negative, we know that all three individual samples are negative. Find the probability
of a positive result for three samples combined into one mixture, assuming the proba-
bility of an individual blood sample testing positive is 0.1 (the probability for the “at-
risk” population, based on data from the New York State Health

Answer 1

the mixture will test negative ONLY if all 3 samples are negative.

the probability that all 3 samples are negative = 0.9*0.9*0.9

Answer 2

the question asks, probability of testing positive

Answer 3

=0.729

so probability that mixture will test positive = 1-0.729 = 0.271

Answer 4

oh yes you are right! Pax,

Answer 5

Thank you all!

Answer 6

P (positive )
= P ( at least one of the 3 blood samples is positive)
= 1 - P (all three are negative) by complement rule
= 1 - (0.9)^3