SOLUTION: 3% of babies in a remote community have a certain blood condition. A new medical test was recently developed to screen babies for this condition. Based on research results, if a ba

Question 1015011: 3% of babies in a remote community have a certain blood condition. A new medical test was recently developed to screen babies for this condition. Based on research results, if a baby has the condition, the test correctly identifies the baby as having the condition 90% of the time. On the other hand, if a baby does not have the condition, the test incorrectly identify the baby as having the condition 12% of the time. Let A be the event that a baby has the condition, B be the event that the medical test identifies the baby of having the condition. (6 Points)
a. What are P(A) and P(Ac)?
b. What are P(B|A) and P(B|Ac)?
c. If a baby is identified by the medical test as having the condition, what is the probability he/she does not have the condition. (Suggestion: To think through the problem, use a probability tree and whether a baby has the condition as the first step to depict what is given. Use the Bayes Theorem to calculate the probability in question. You do not need to include the tree in your submission.)
Any help would be greatly appreciated - thanks

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
I will denote the complement by A', not Ac.
a. P(A) = 0.03, while P(A') = 0.97
b. P(B|A) = P(AB)/P(A)) = = 0.90
P(B|A') = P(A'B)/P(A') = = 0.12

c. We are looking for P(A'|B).
P(A'|B) = P(A'B)/P(B) = P(A'B)/(P(A'B)+P(AB)) = = 194/239.
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