Question Help probability of a randomly selected adult in one country being infe

Question

Question Help probability of a randomly selected adult in one country being infected with a certain virus is 0.004. In tosts for the vinus, blood samples from 16 people are combined What is the sample tests positive for the virus? is it unilkely for such a combined sample to test postive? Note that the combined sample tosts positive if at least one person has the vinus are combined What is the probability that the combined The probabilly that the combined sample will teset poaitive is Round to three decimal places as needed.)

Explanation / Answer

p = probability of infected with virus = 0.004.

q = probability of not infected with virus = 1 - p = 0.996

n = 16

Binomial distribution.

Probability that combined sample will test positive = Probability that at least one person has virus.

= 1 - Probability that nobody has virus out of 18 persons

= 1 - q^n

= 1 - (0.996)^16  

= 1 - 0.9378

= 0.0622.

= 0.062( Three decimals)

So, it is likely that the combined sample tests positive for the virus.

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