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 ?
(A) 7/10
(B) 8/11
(C) 1/3
(D) 1/2

Answer: (C)
Explanation: Let total number of people

= x 

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 

Probability,

= 0.09x / 0.27x
= 1/3 

Option (C) is correct.
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