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  • A screening test is carried out to detect a certain disease. It is found that 12% of the positive reports and 15% of the negative reports are incorrect. Assuming that the probability of a

A screening test is carried out to detect a certain disease. It is found that 12% of the positive reports and 15% of the negative reports are incorrect. Assuming that the probability of a person getting positive report is 0.01 , the probability that a person tested gets an incorrect report is getting positive report is 0.01 , the probability that a person tested gets an incorrect report is

Option: 1

0.0027


Option: 2

0.0173


Option: 3

0.1497


Option: 4

0.2100


Answers (1)

best_answer

Let              A={person gets an incorrect report }

\mathrm{E_1=\{\text { person getting } \text { +ve report }\}}\Rightarrow \mathrm{P(E_{1})}=0.01

                                            \mathrm{E_2}=\text { \{person getting -ve report}\} \\

\mathrm{ \Rightarrow \quad P\left(E_2\right)=0.99}

     \mathrm{P\left(A /E_1\right)=P(+ \text { ve report is incorrect })} 

                          =0.12

So By Law of total probability 

                   \mathrm{\left.P(A)=P\left(E_1\right) \cdot P\left(A / E_1\right)+P\left(E_2\right) \cdot P A / E_2\right)}

                                \begin{aligned} & =(0.01)(0.12)+(0.99)(0.15) \\ \\& =0.1497 \end{aligned}                   

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HARSH KANKARIA

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