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KVPY Sample Paper KVPY Stream-SX Model Paper-9

  • question_answer
    The change that doctor A will diagnose disease X correctly is \[60%\]the change that a patient of doctor A dies after correct treatment is\[~75%\]while it is \[80%\]after wrong Diagnosis. A patient of doctor A having disease X dies. The probability that his disease  is correctly diagnosed is

    A) \[\frac{8}{17}\]                         

    B) \[\frac{9}{17}\]

    C) \[\frac{11}{17}\]                                   

    D) \[\frac{6}{17}\]

    Correct Answer: B

    Solution :

    let A denote the event of correct diagnosis and E the event of patients death. It is given that 
    \[P(A)=\frac{60}{100},P(\overline{A})=\frac{40}{100}\]
    \[P(E/A)=\frac{75}{100}\] and \[P\left( \frac{E}{\overline{A}} \right)=\frac{80}{100}\]
    By Bayes? theorem
    \[P\left( \frac{A}{E} \right)=\frac{P(A)P(E/A)}{P(A)P(E/A)+P(\overline{A})P(E/\overline{A})}\]\[=\frac{\frac{60}{100}+\frac{75}{100}}{\frac{60}{100}\times \frac{75}{100}+\frac{40}{100}\times \frac{80}{100}}\]
    \[=\frac{\frac{3}{5}\times \frac{3}{4}}{\frac{3}{5}\times \frac{3}{4}+\frac{2}{5}\times \frac{4}{5}}=\frac{9}{17}\]


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