Question

The probability of a randomly selected adult in one country being infected with a certain virus is 0.0050.005. In tests for the​ virus, blood samples from 2626 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

Answer:

0.1222 or 12.22%

Yes, it is unlikely.

Step-by-step explanation:

If the probability of someone being infected is 0.005, then the probability of someone not being infected is 0.995. In order for the combined sample to test negative (N), all of the 26 people must test negative. Thus, the probability that the combined sample tests positive is:

$P(Sample = P) = 1 -P(N=26)\\P(Sample = P) = 1 -0.995^{26}\\P(Sample = P) = 0.1222=12.22\%$

There is a 0.1222 or 12.22% probability that the combined sample tests positive, which is unlikely to occur.