Question

The probability of a randomly selected adult in one country being infected with a certain virus is 0.0030.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.

The probability that the combined sample will test positive is ___? (3 decimals)

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

Answer 1

solution:-

given that p = 0.0030 , n = 21

the probability that the combined sample tests positive for the​ virus

P(x ≥ 1) = 1 - P(x = 0)

= 1 - (21C0 * 0.0030^0 * (1-0.0030)^(21-0))

= 1 - (21!/(0!(21−0)!) * 0.0030^0 * (1-0.0030)^(21-0))

= 1 - (1*0.0030^0 * (1-0.0030)^(21-0))

= 1 - 0.939

= 0.061

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

we can say that

=> 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