When doing blood testing for a viral infection, the procedure can be made more e

Question

When doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial samples of different 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 for the virus is 0.07. Round the answer to four decimal place accuracy. prob-

Explanation / Answer

P( single test is positive) = .07

P( the mixture is positive)

= 1- P(the mixture is not positive)

= 1- P(Each of the 3 individuals sample is not positive)

= 1- (1-.07)^3

= .1956

The probability that the mixture of 3 samples is positive is .1956

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