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TS EAMCET 14-Sep-2020 Shift 2 Solved Paper

Section: Mathematics

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Question : 38 of 160

Marks: +1, -0

A diagnostic test has the probability

0.95

of giving a positive result when applied to a person suffering from a certain disease, and a probability

0.10

of giving a positive result when given to a non-sufferer. It is estimated that

0.5\%

of the population are suffering from the disease. If this test is now administered to a person from this population about whom there is no information relating to the incidence of this disease and the test gives a positive result, then the probability that he is a sufferer, is

0.94545
0.2194
0.0455
0.9499

Solution:

Consider the events,

E_{1}=

Person suffering from a certain disease

E_{2}=

Person are not suffering from a certain disease

A=

Diagnostic test is positive

P(E_{1}) =0.5\% \quad P(E_{2})=99.5\%

P(A/E_{1}) =0.95 P(A/E_{2})=0.10

Required probability

P(E_{1}/A)= \frac{P(E_{1}) \times P(A/E_{1})}{P(E_{1}) \times P(A/E_{1})+P(E_{2}) \times P(A/E_{2})}

= \frac{0.005 \times 0.95}{(0.005 \times 0.95)+0.995 \times 010}

= \frac{0.00475}{0.00475+0.0995} = \frac{0.00475}{010425} = \frac{475}{10425} = 0.0455

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