Question

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?

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