GATE | Sudo GATE 2020 Mock III (24 January 2019) | Question 59
Doctors have devised a test for leptospirosis that has the following property:
For any person suffering from lepto, there is a 90% chance of the test returning positive. For a person not suffering from lepto, there is an 80% chance of the test returning negative. It is known that 10% of people who go for testing have lepto. If a person who gets tested gets a +ve result for lepto (as in, the test result says they have got lepto).
What is the probability that they actually have lepto ?
Explanation: Let total number of people
Number of Persons who have lepto
= 0.9*0.1x = 0.09x
Number of persons who gets tested gets a +ve result for lepto
= 0.1x*0.9 + 0.9x*0.2 = 0.27x
= 0.09x / 0.27x = 1/3
Option (C) is correct.
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