A genetic test is used to determine if people have a predisposition for thrombosis, which is the formation of a blood clot inside a blood vessel that obstructs the flow of blood through the circulatory system. it is believed that 3% of people actually have this predisposition. the genetic test is 99% accurate if a person actually has the predisposition, meaning that the probability of a positive test result when a person actually has the predisposition is 0.99. the test is 98% accurate if a person does not have the predisposition. what is the probability that a randomly selected person who tests positive for the predisposition by the test actually has the predisposition?

Question

Biology

Fawn

16 July, 17:40

A genetic test is used to determine if people have a predisposition for thrombosis, which is the formation of a blood clot inside a blood vessel that obstructs the flow of blood through the circulatory system. it is believed that 3% of people actually have this predisposition. the genetic test is 99% accurate if a person actually has the predisposition, meaning that the probability of a positive test result when a person actually has the predisposition is 0.99. the test is 98% accurate if a person does not have the predisposition. what is the probability that a randomly selected person who tests positive for the predisposition by the test actually has the predisposition?

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Devan Haas · Answer 1

The probability that a randomly selected person who tests positive for the predisposition by the test actually has the predisposition is

P (A | B) = P (B | A) P (A) / P (B) so P (Disease | positive) = P (positive |

disease) P (disease) / P (positive) = (0.99) (0.03) / P (positive)

P (Positive) = P (Positive | disease) P (disease) + P (Positive | no disease

) P (no disease)

= (0.99) (0.03) + (0.02) (0.97) = 0.0491

so P (Disease | positive) = (0.99) (0.03) / (0.0491) =.6