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 17 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

The probability that the combined sample will test positive is?

Answer 1

P(a person is infected with virus) = 0.006

P(a person is not infected with virus) = 1 - 0.006 = 0.994

P(combined sample will test positive is) = P(at least  one person has the virus)

= 1 - P(none of the 17 people has the virus)

= 1 - 0.994¹⁷

= 0.0972

An event can be be considered unlikely is the probability of occurrence is less than 0.05. Here, the probability of the event is greater than 0.05 and hence, it is not unlikely for such a combined sample to test​ positive.