The probability of a randomly selected adult in one country being infected with
ID: 3202249 • Letter: T
Question
The probability of a randomly selected adult in one country being infected with a certains virus is 0.004. In tests for the virus, blood samples from 18 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 ___
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The probability or a randomly selected ad ut In one country being infected acertain virus 0.004. In tests tor the Tus, blood samples trom 18 people are combined. What Is the probability that the combned sample tests positve for the virus? ls it unikely for such a combined sample to test positve? Note that the combined sample tests positive If at least one person has the viru The probability that the combined sample will test positive is LI (Round to three decimal places as needed.)Explanation / Answer
Let
p = probability of infected with virus = 0.004.
q = probability of not infected with virus = 1 - p = 0.996
n = 18
Binomial distribution.
Probability that combined sample will test positive = Probability that at least one person has virus.
= 1 - Probability that nobody has virus out of 18 persons
= 1 - qn
= 1 - (0.996)18
= 1 - 0.9304
= 0.0696.
So, it is likely that the combined sample tests positive for the virus.
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