Problema Solution
A new medical screening test is used to detect a rare, non-life-threatening condition. If a person has this condition, the test always detects it. Approximately 0.9% of the population has the condition. Over many trials, the test returns a positive result 5% of the time. Julio takes the test and gets a positive result. To the nearest tenth of a percent, what is the probability that Julio actually has the condition?
Answer provided by our tutors
We will use the Bayes Theorem to solve this problem.
Bayes’ Theorem says that for any two events A and B,
P(A/B) = (P(A)*P(B/A))/P(B).
In our case we have the following events:
A: "Julia has the condition"
B: "Julie tested positive"
P(A/B) is the probability that we need to find (Julio has the condition assuming he testes positive)
P(A) = 0.009 (or 0.9% of the population has the disease)
P(B) = 0.05 or 5%
P(B/A) = 1 since if a person has this condition, the test always detects it
Now we can find P(A/B) by plugging the values into the formula:
P(A/B) = (0.009*1)/0.05
P(A/B) = 0.18 or 18%
The probability that Julio actually has the condition on the condition that he tested positive is 18%.