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JEE Main & Advanced Sample Paper JEE Main Sample Paper-37

  • question_answer
    One percent of the population suffers from a certain disease. There is blood test for this disease, and it is \[99%\] accurate, in other words, the probability that it gives the correct answer is \[0.99\], regardless of whether the person is sick or healthy. A person takes the blood test, and the result says that he has the disease. The probability that he actually has the disease, is-

    A) \[0.99%\]                    

    B) \[25%\]

    C) \[50%\]                       

    D) \[75%\]

    Correct Answer: C

    Solution :

      A: blood result says positive about the disease \[{{B}_{1}}:\]Person suffers from the disease\[\therefore P({{B}_{1}})=\frac{1}{100}\] \[{{B}_{2}}:\] person does not suffer\[\therefore P({{B}_{2}})=\frac{99}{100}\] \[P(A/{{B}_{1}})=\frac{99}{100},\,\,P(A/{{B}_{2}})=\frac{1}{100}\] \[P({{B}_{1}}/A)=\frac{P({{B}_{1}})P(A/{{B}_{1}})}{P({{B}_{1}}).P(A/{{B}_{1}})+P({{B}_{2}}).P(A/{{B}_{2}})}\] \[=\frac{\frac{1}{100}\cdot \frac{99}{100}}{\frac{1}{100}\cdot \frac{99}{100}+\frac{99}{100}\cdot \frac{1}{100}}=\frac{99}{2\cdot 99}=\frac{1}{2}=50%\]


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