# Thread: Probability with combined tests

1. ## Probability with combined tests

Hi

When doing blood testing for HIV infections the procedure can be made more cost effective 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 probability of an individual blood sample testing positive is 0.1 .

2. Originally Posted by shogunhd
Hi

When doing blood testing for HIV infections the procedure can be made more cost effective 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 probability of an individual blood sample testing positive is 0.1 .
The probability of a positive result is 1 minus the probability all three are negative, which gives:

p(1 or more +)=1-p(-)^3=1-0.9^3

RonL