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

Question

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)

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Kim Chi 3 years 2021-08-26T10:56:03+00:00 1 Answers 5 views 0

Answers ( )

  1. thuthuy
    0
    2021-08-26T10:58:00+00:00
    Reply

    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 \frac{950}{950+270} .

    • \frac{950}{1220} ⇒ 0.7786 ≈ 0.77

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