All interns for Comcast are required to be tested for drug use. The imperfect test gives positive results (indicating drug use) for 80% of all interns who actually use drugs but also (incorrectly) for 3% of those who do not use drugs. Suppose that only 10% of all of these interns actually use drugs.
If an intern is tested negative, what is the probability that he/she uses drugs?

0.0224 or 2.24%

Step-by-step explanation:

The probability that an intern uses drugs, given that the test is negative, is determined by  the probability of false negative divided by the probability of a negative (true or false).

A false negative occurs when an intern who uses drugs (10%) takes the test and gets a negative. Since the test gets it right 80% of the time, the probability of this happening is:

A true negative occurs when an intern who does not use drugs (90%) takes the test and gets a negative. Since the test gets it wrong 3% of the time, the probability of this happening is:

Therefore, the probability that an intern uses drugs, given that the test is negative is:

The probability is 0.0224 or 2.24%.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.