Originally Posted by windy_city
Suppose it is assumed that about 5% of the general population use drugs. You employ a test that is 95% accurate, which we?ll say means that if the individual is a user, the test will be positive 95% of the time, and if the individual is a nonuser, the test will be negative 95% of the time. A person is selected randomly and given the test. It is positive. What does such a result suggest? Would you conclude that the individual is highly likely to be a drug user?
Hmm.. for sure my intuitive thought told me that there is a 95% of chance that the individual is a drug user.
But later on, I changed my mind. Here's my attempted reasoning: (sorry for providing reasoning, but those who want to try themselves can just skip all the reasonings)
1. When you choose an individual randomly, there's 5 % chance of getting a drug user and 95% chance of getting a nonuser.
2. Users and nonusers are mutually exclusive.
*3.1.1 For users, since 95% of the time we get right result, that means there are 4.75% of population that will show positive results and IS drug user.
*3.1.2 For users, since 5% of the time we get wrong result, that means there are 0.25% of the population that will show negative results but IS drug user.
*3.2.1 For non-users, since 95% of the time we get right result, there are 90.25% of the population that will show negative result and IS NOT drug user.
*3.2.2 For non-users, since 5% of the time we get wrong result, there are 4.75% of population that will show positive results but IS NOT drug user.
Now refer to 3.1.1 and 3.2.2. When you get positive result, there is actually an equal
chance of getting a user or nonuser.
If my answer is wrong, can anyone kindly point out which part of my reasoning is wrong.
p/s: I am a medical student.