Sree Leela thinks she may be allergic to Bengal gram and takes a test that is known to give the following result:
For people who really do have the allergy, the test says “Yes” 90% of the times.
For people who do not have the allergy, the test says “Yes” 15% of the times.
If 2% of the population has the allergy and SreeLeela’s test says “Yes”, then the chance that chance that SreeLeela does really have the allergy is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

1/11

Cannot be determined from the given data

1/9

6/55

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Let A denote the event that the test says “Yes”. Consider two hypothesis;
$H_{0}$ - SreeLeela has the allergy;
$H_{1}$ - SreeLeela does not have the allergy;
Then, $P (H_{0}) = 0.02, P (H_{1}) = 0.98, P (A) (H_{0}) = 0.9, P (A) (H_{1}) = 0.15$
By the Bayes rule

$P (H_{0} | A) = \frac{P (A | H_{0}) P (H_{0})}{P (A | H_{0}) P (H_{0}) + P (A | H_{1}) P (H_{1})} = \frac{0.9.0.02}{0.9.0.02 + 0.15.0.98} = \frac{18}{165} = \frac{6}{55}$