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A medical test has a 95% accuracy of detecting a Condition Z if the person has it. It also has a 97% chance to indicate that the person does not have the condition if they really don't have it. If the incidence rate of this disease is 10 out of every 100: What is the probability that a person chosen at random will both test positive and actually have the disease (i.e., get a true positive)

Respuesta :

Answer:

0.77

Step-by-step explanation:

According to the Question,

Let, We have 10000 patients & If the incidence rate is 10 out of 100, then 1000 people will have the disease.

  • Given, A medical test has a 95% accuracy of detecting Condition Z if the person has it. Thus, Out of those 1000, 950 will test positive.
  • And, It also has a 97% chance to indicate that the person does not have the condition if they really don't have it

        So, Out of the 9000 people who don't have the disease, 3%

       that is, 270 People, will get a false positive.

Thus, the probability that a person is chosen at random will both test positive and actually have the disease is [tex]\frac{950}{950+270}[/tex] .

  • [tex]\frac{950}{1220}[/tex] ⇒ 0.7786 ≈ 0.77

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