Question 1084666: A medical test has a 95% accuracy of detecting a Condition Z if the person has it. It also has a 97% chance to indicate that the person does not have the condition if they really don't have it. If the incidence rate of this disease is 10 out of every 100:
What is the probability that a person chosen at random will both test positive and actually have the disease (i.e., get a true positive)?
What is the probability that a person chosen at random will test positive but not have the disease (i.e., get a false positive)?
Answer by jorel1380(3719)   (Show Source):
You can put this solution on YOUR website! Consider 10000 patients.
If the incidence rate is 10 out of 100, then 1000 people will have the disease.
Out of those 1000, 950 will test positive. Out of the 9000 people who don't have the disease, 3%, or 270, will get a false positive. Therefore:
The possibility that a person who tests positive actually has the disease is 950/950+270, or 0.77868852459016393442622950819672.
The possibility that a person will get a false positive is 100-97, or 3%. ☺☺☺☺
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