Using Composite Blood Samples When doing blood testing for H

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 these people are combined and the mixture tests negative, we know that alt three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture, assuming the probability of an individual blood sample testing positive is 0.1 (die probability for the at-risk\" population, based on data from the New York State Health Department).

Solution

p=0.1

n=3

P(1 negative) = 1-0.1 = 0.9

P(3 negative) = 0.9^3 = 0.729

P (test positive) = 1-0.729 = 0.271 or 27.1%