A genetic test is used to determine if people have a predisposition for thrombos

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 has the predisposition and 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 actually has the predisposition? (In other words, what is the probability of a true positive result?) Do not give your answer as a percentage chance, but rather as a decimal probability (i.e., 0.xxx). Answer:

Explanation / Answer

probabilty of predisposition =P(P) =0.03

probability of +ve test result=P(+ve) =P(P)*P(+ve|P)+P(Pc)*P(+ve|Pc)=0.03*0.99+(1-0.03)*(1-0.98)=0.0491

hence probabilty of having predisposition , given tests postive=P(P|+ve)=P(P)*P(+ve|P)/P(+ve) =0.03*0.99/0.0491

=0.6049

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