Case-Study 2: Read the following passage and answer the questions given below By examine the test, the probability that a person is diagnosed with CORONA when he is actually suffering from it, is 0.99. The probability that the doctor incorrectly diagnosed a person to be having CORONA, on the basis of test reports, is 0.001. In a certain city, 1 in 1000 persons suffers from CORONA. A person is selected at random
and is diagnosed to have CORONA.
On the basis of above information, answer the following questions.
(i) What is the P (CORONA is diagnosed, when the person actually has CORONA) and the P (CORONA is diagnosed, when the person has not CORONA)?
(ii) What is P (CORONA is diagnosed)?
(iii) What is the P (Person has CORONA given CORONA is diagnosed)?

Question

Case-Study 2: Read the following passage and answer the questions given below By examine the test, the probability that a person is diagnosed with CORONA when he is actually suffering from it, is 0.99. The probability that the doctor incorrectly diagnosed a person to be having CORONA, on the basis of test reports, is 0.001. In a certain city, 1 in 1000 persons suffers from CORONA. A person is selected at random
and is diagnosed to have CORONA.
On the basis of above information, answer the following questions.
(i) What is the P (CORONA is diagnosed, when the person actually has CORONA) and the P (CORONA is diagnosed, when the person has not CORONA)?
(ii) What is P (CORONA is diagnosed)?
(iii) What is the P (Person has CORONA given CORONA is diagnosed)?

Accepted Answer

Let  = event that the doctor diagnoses CORONA1 = event that the person selected is suffering from CORONA1 = event that the person selected is suffering from CORONAWe have, P (Person suffering from CORONA)=PE1=11000=0.001Also, PE2=1−PE1=1−11000=9991000=0.999(i)The required probabilities=PEE1=99100=0.99and PEE2=11000=0.001(ii)∴Required probability =P(E)=∑i=12 PEiPEEi=PE1PEE1+PE2PEE2=0.001×0.99+0.999×0.001=0.00099+0.000999=0.001989(iii)∴ Required Probability =PE1E=PE1PEE1PE1PEE1+PE2PEE2=0.001×0.990.001×0.99+0.999×0.001=0.000990.00099+0.000999=0.000990.001989=110221

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App