A rare disease a ects 2% of the population. A test has a sensitivity of 97%, i.e

Question

A rare disease a ects 2% of the population. A test has a sensitivity of 97%, i.e., it will
give a positive result 97% of the time that a person actually has the disease. The same
test also has a speci city of 99%, i.e., it will give a negative result 99% of the time when
a person does not have the disease. Denote the event that a randomly selected person
has a disease by D, and the event that a randomly selected person has a positive blood
test by T.
Q 1 .Calculate the probability that a randomly selected person has the disease, given that they have a positive blood test.

Explanation / Answer

Q1. P(D|T) = P(D and T)/P(T)

= P ( tested positive and having disease)/P(tested positive)

= 0.02x0.97/(0.02x0.97 + 0.98x0.01)

= 0.6644

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