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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) =
= =
= 0.605 .