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Answer:
The probability of having a positive test on a non-sick person is 24.32%.
Step-by-step explanation:
The probability of having a POS and not having tuberculosis, can be defined as the probability of getting a false positive.
The amount of positive test will be
1) The positive test of sick persons
[tex]P(test=pos;person=sick)=0.744*0.05=0.0372[/tex]
2) The positive test of not-sick persons (false positives)
[tex]P(test=pos;person=sick)=(1-0.744)*0.95=0.256*0.95=0.2432[/tex]
The amount of positive test will be
1) The negative test of non-sick persons
[tex]P(test=neg;person=non-sick)=0.7653*0.95=0.727[/tex]
2) The negative test of sick persons (false negatives)
[tex]P(test=neg;person=non-sick)=(1-0.7653)*0.05=0.2347*0.05=0.0117[/tex]
The probability of having a positive test on a non-sick person is 0.24 = 24.32%.
Suppose that,
The population of adults that is taking the test, 5% have tuberculosis.
The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time.
Suppose that, POS stands for the test gives a positive result and S means that the adult really has tuberculosis.
We have to find,
What is the probability of an adult getting a POS result and truly NOT having tuberculosis.
According to the question,
The probability of having a POS and not having tuberculosis, can be defined as the probability of getting a false positive.
- The amount of positive test will be,
The positive test of sick persons,
[tex]p (test; positive, person=sick) = (0.744).(0.05) = 0.372[/tex].
The positive test of non sick persons (false positives),
[tex]p (test; positive, person=sick) = (1-0.744)(0.95) = 0.24[/tex]
- The amount of positive test will be,
The negative test of non-sick persons,
[tex]p (test; negative, person=non sick) = (0.7653).(0.95) = 0.727[/tex]
The negative test of sick persons (false negatives),
[tex]p (test; positive, person=sick) = (1-0.7653)(0.05) = 0.0117[/tex]
Hence, The probability of having a positive test on a non-sick person is 0.24 = 24.32%.
For more information about Binomial distribution click the link given below.
https://brainly.com/question/24750931
