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.

1. The probability that the combined sample will test positive is ?

2. Is it unlikely for such a combined sample to test​ positive?

A. 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.

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

C. It is unlikely for such a combined sample to test​ positive, because the probability that the combined sample will test positive is greater than 0.05.

D. It is unlikely for such a combined sample to test​ positive, because the probability that the combined sample will test positive is less than or equal to than 0.05.

Answer 1

Ans:

Use Binomial distribution with n=17 and p=0.006

1)

P(combined test is positive)=P(at least one is positive)

=1-P(none is positive)=1-(1-0.006)^17=0.0972

2)

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.