Question
6. A rare and sever form of anemia occurs at a rate of one case per...
6. A rare and sever form of anemia occurs at a rate of one case per thousand people in the general population. Simple diagnostic test for anemia has the following property: If the person tested actually has anemia, then the probability of a positive test is .90. If the person tested does not have this anemia, then the probability of a negative test is .95. Given a positive test result, what is the likelihood that the person actually has anemia?
Homework Answers
Answer #1
X : Event of a person having anemia
: Event of a person not having anemia
anemia occurs at a rate of one case per thousand people in the general population
P(X) = Probability of of a person having anemia = 1/1000 = 0.001
PT : Event of positive test.
If the person tested actually has anemia, then the probability of a positive test is .90 i,e
P(PT |X) = 0.90
:
Event of (not positive) negative test
If the person tested does not have this anemia, then the probability of a negative test is .95
P(
|
) = 0.95
P(PT |
) = 1 - P(
|
) = 1 - 0.95 = 0.05
Given a positive test result, likelihood that the person actually has anemia = P(X|PT)
By Bayes Theorem,
Given a positive test result, the likelihood that the person actually has anemia = 0.0177
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