I would really appreciate if someone could help me out.

A test for a certain drug produces a false negative 5% of the time and false positive 8% of the time. Suppose 12% of the employees at a certain company use the drug.

If an employee at the company tests positive, what is the probability that he or she does not use the drug?

(1-.12) * .08 = ?

PsyDAG,

The 1 is equivalent to 100 right since it is 12 out of 100? I had 0.88*0.12.
I was totally wrong.

To solve this problem, we can use Bayes' theorem. Let's break down the problem step by step:

Step 1: Understand the given information:
We are given the following probabilities:
- P(false negative) = 0.05 (the probability of testing negative when the person actually uses the drug)
- P(false positive) = 0.08 (the probability of testing positive when the person does not use the drug)
- P(use drug) = 0.12 (the probability that an employee uses the drug)

We are asked to find the probability of not using the drug given a positive test result.

Step 2: Define the events:
Let's define the events:
- A: An employee uses the drug
- B: An employee tests positive

What we need to find is P(not using drug | positive test), which can be written as P(~A | B).

Step 3: Apply Bayes' theorem:
Bayes' theorem states that:
P(A | B) = (P(B | A) * P(A)) / P(B)

In our case, we need to find P(~A | B), which can be written as:
P(not using drug | positive test) = (P(positive test | not using drug) * P(not using drug)) / P(positive test)

Step 4: Calculate the probabilities:
Now, let's substitute the given probabilities into Bayes' theorem:
P(not using drug | positive test) = (P(positive test | not using drug) * P(not using drug)) / P(positive test)
P(~A | B) = (P(B | ~A) * P(~A)) / P(B)

Given:
P(B | ~A) = 0.08 (false positive rate)
P(~A) = 1 - P(A) = 1 - 0.12 = 0.88 (the probability of not using the drug)

To calculate P(B), we can use the law of total probability, which states that the probability of an event B can be calculated as the sum of the probabilities of B occurring under each possible condition:

P(B) = P(B | A) * P(A) + P(B | ~A) * P(~A)

Substituting the given values:
P(B) = (0.05 * 0.12) + (0.08 * 0.88)

Now, we can solve for P(~A | B):
P(~A | B) = (P(B | ~A) * P(~A)) / P(B)

Substituting the given values:
P(~A | B) = (0.08 * 0.88) / [(0.05 * 0.12) + (0.08 * 0.88)]

By calculating this expression, you will find the probability that an employee does not use the drug given a positive test result.