Question

The probability of a randomly selected adult in one country being infected with a certain virus is 0.006 . In tests for the​ virus, blood samples from 21 people are combined. What is the probability that the combined sample tests positive for the​ virus? Is it unlikely for such a combined sample to test​ positive? Note that the combined sample tests positive if at least one person has the virus.

Answer 1

Given,

The probability that in one country a randomly selected adult being infected with a certain virus is 0.006. There are 21 blood samples of people which are combined.

Sample size (n)=21

The probability (p)=0.006

Consider X is a random variable denotes the number blood sample of people which has the virus

X will follow Binomial distribution with parameters n=21 and p = 0.006

X ~ Bin( 21 , 0.006)

The probability that the combined sample tests positive for the​ virus i.e.  at least one person has the virus P(X 1)

  

  

The probability that the combined sample tests positive for the​ virus is 0.1187.

It is not unlikely for such a combined sample to test​ positive, because the probability that the combined sample will test positive is greater than 0.05.