Two percent (0. 02) of all individuals in a certain population are carriers of a

Question

Two percent (0. 02) of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 97% detection rate for carriers and a 96% chance of not detecting the disease in non-carriers. Suppose an individual is selected at random from the population and tested for the disease. a) What is the probability that the selected individual is a carrier and tests negative? b) Given the individual is a non-carrier, what is the probability that the individual tests positive?

Explanation / Answer

a) Probability that the selected individual is a carrier and tests negative

= Probability that the individual is a carrier * Probability that the individual is tested negative given that he is a carrier

= 0.02*(1- 0.97)

= 0.0006

Therefore 0.0006 is the required probability here.

b) Probability that the individual tests positive given that he is a non carrier

= 1 - Probability that the individual tests negative given he is a non carrier

= 1- 0.96

= 0.04

Therefore 0.04 is the required probability here.

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