Find the probability of a positive result for five samples combined into one mixture, assuming the probability of an individual blood sample testing positive for the virus is 0.07.

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 five people are combined and the mixture tests negative, we know that all five individual samples are negative. Find the probability of a positive result for five 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.

Answer 1

.07 = P(+)

P(-)= 1-.07= .93

P(5-)= .93^5=.695688= 69.5688% chance all 5 negative