SOLUTION: A certain disease occurs in 1 out of every 150 Americans. A test used to diagnose the disease has a false positive rate of 3% and a false negative rate of 6%. Find the probability

Question 271656: A certain disease occurs in 1 out of every 150 Americans. A test used to diagnose the disease has a false positive rate of 3% and a false negative rate of 6%. Find the probability that a person has the disease, given that they test positive, and the probability that a person does not have the disease, given that they test negetive.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Without disease: 149/150=.9933 of the population with .9933*.03=.0298 testing positive and .9933*.97=.9635 testing neg.
With disease: 1/150=.0067 of the population with .0067*.94=.0063 testing positive and .0067*.06=.0004 neg.
.
.0298 + .0063 = .0361 prob of anyone in the population testing pos.
The probability that a person has the disease, given that they test positive:.0063/.0361=.1745
.
.9635 + .0004 = .9639 Prob of anyone in the population testing neg.
The probability that a person does not have the disease, given that they test negative: .9635/.9639=.9996
.
Ed
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