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KVPY2020MathematicsProbability

In medical diagnostics for a disease, sensitivity (denoted a) of a test refers to the probability that a test result is positive for a person with the disease whereas specificity (denoted b) refers to the probability that a person without the disease test negative. A diagnostic test for influenza has the values of a = 0 . 9 and b = 0 . 9 . Assume that the prevalence of influenza in a population in 50 % . If a randoml

Options

  1. A0 . 01
  2. B0 . 02
  3. C0 . 05
  4. D0 . 10

Correct answer

D. 0 . 10

Step-by-step solution

Let I be the evert that person has infected P be the evert that test result is positive P   I / P ¯ = P I   P P ¯ / I P I   P P ¯ / I + P I ¯   P P ¯ / I ¯ P I = P I ¯ = 1 2 P P / I = 9 10   &   P P ¯ / I ¯ = 9 10 P I / P ¯ = 1 2 × 1 10 1 2 × 1 10 + 1 2 × 9 10 = 1 10 = 0 . 1

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