SOLUTION: 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 24 people are combined. Wha

Algebra ->  Probability-and-statistics -> SOLUTION: 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 24 people are combined. Wha      Log On


   

Question 1185500: 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 24 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 by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
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 24 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.
~~~~~~~~~~~~~~~~ 

Let me re-formulate the problem in clear short EQUIVALENT form.


       If the probability of the event is 0.004, what is the probability 
       that in 24 independent trials it will happen at least once ?


The probability that it will not happen, is  0.996.


The probability that it will not happen in 24 trials is  0.996%5E24 = 0.908289.


The probability that it will happen at least once in 24 trial is the complement to it


    P = 1 - 0.996%5E24 = 1 - 0.908289 = 0.091711.    ANSWER

Solved.