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The probability of a randomly selected adult in one country being infected with a certain virus is 0.004. In tests for the​ virus, blood samples from 15 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.

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Answer:

The probability is [tex]P(R) = 0.0583 [/tex]

Step-by-step explanation:

From the question we are told that

  The probability that selected adults are affected by virus is  p =  0.004

  The probability that adults are not affected by virus is  [tex]q= 1- p = 1-0.004 = 0.996[/tex]

    The sample size is  n =  15

 Generally from the question we are told that    

The probability that the combined sample tests positive is equal to the probability that  at least one person test positive for the  virus

So  

The probability that the combined sample tests positive for the​ virus is equal to  

  1- the probability that non of the adults selected tested positive for the virus

Generally the probability that  non of the adults selected tested positive for the virus is  

      [tex]P(k) = q^n[/tex]

=>    [tex]P(k) = q^{15}[/tex]

=>    [tex]P(k) = 0.996^{15}[/tex]

=>    [tex]P(k) =  0.9417 [/tex]

The probability that the combined sample tests positive for the​ virus is mathematically represented as

        [tex]P(R) = 1 - P(k)[/tex]

=>     [tex]P(R) = 1 - 0.9417 [/tex]

=>     [tex]P(R) = 0.0583 [/tex]

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