After your yearly checkup, the doctor has bad news and good news. The bad news i
ID: 3825414 • Letter: A
Question
After your yearly checkup, the doctor has bad news and good news. The bad news is that you tested positive for a serious disease and that the test is 99% accurate (i.e., the probability of testing positive when you do have the disease is 0.99, as is the probability of testing negative when you don't have the disease). The good news is that this is a rare disease, striking only 1 in 10,000 people of your age. Why is it good news that the disease is rare? What are the chances that you actually have the disease?Explanation / Answer
Answer:
Consider an example of 10,000 people. Of them, 1 being has the disease. If 10,000 populations take the test, there is a 1% chance of testing optimistic if you DON'T have the illness so, 100 populations will test positive.
P (test disease) = 0.99
P (¬test|¬disease) = 0.99
P (disease) = 0.0001
P (disease test) = P (test disease) P (disease) /
(P (test disease) P (disease) + P (test|¬disease) P (¬disease))
= 0.99 × 0.0001 / (0.99 × 0.0001 + 0.01 × 0.9999)
= 0.009804.