Answer:
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%.