Answer:
Required Probability = 0.605
Step-by-step explanation:
Let Probability of people actually having predisposition, P(PD) = 0.03
Probability of people not having predisposition, P(PD') = 1 - 0.03 = 0.97
Let PR = event that result are positive
Probability that the test is positive when a person actually has the predisposition, P(PR/PD) = 0.99
Probability that the test is positive when a person actually does not have the predisposition, P(PR/PD') = 1 - 0.98 = 0.02
So, probability that a randomly selected person who tests positive for the predisposition by the test actually has the predisposition = P(PD/PR)
Using Bayes' Theorem to calculate above probability;
P(PD/PR) = [tex]\frac{P(PD)*P(PR/PD)}{P(PD)*P(PR/PD)+P(PD')*P(PR/PD')}[/tex]
= [tex]\frac{0.03*0.99}{0.03*0.99+0.97*0.02}[/tex] = [tex]\frac{0.0297}{0.0491}[/tex] = 0.605 .
