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 four people are combined and the mixture tests negative, we know that all four individual samples are negative. Find the probability of a positive result for four samples combined into one mixture, assuming the probability of an individual blood sample testing positive for the virus is 0.11.

Answer 1

Answer:

0.3726 is the required probability.                                

Step-by-step explanation:

We are given the following information:

We treat blood sample testing positive for the virus as a success.

P( blood sample testing positive for the virus ) = 0.11

Then the number of blood sample follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 4

We have to evaluate the probability of a positive result for four samples combined into one mixture mean that atleast one of the blood sample must be positive for virus.

$P(x \leq 1)\\1 - P(x = 0)\\= 1 - \binom{4}{0}(0.11)^0(1-0.11)^4\\=1-0.6274\\= 0.3726$

0.3726 is the probability of a positive result for four samples combined into one mixture.