Question

In the drug testing, assume there are three possible test results: positive, negative, and inconclusive. for a drug user, the probabilities of these outcomes are 0.65, 0.06, and 0.29. for a nonuser, they are 0.03, 0.72, and 0.25. the prior probability of being a drug user is still 0.05. what is the posterior probability that the athlete is a drug user, given that her test result is positive? group of answer choices

O 0.533
O 0.004
O 0.467
O 0.996

Answer 1

The posterior probability that the athlete is a drug user, given that her test result is positive, is found using Bayes' theorem and is approximately 0.533.

Step-by-step explanation:

The question asks for the posterior probability that an athlete is a drug user given a positive test result.

Let's first determine the various probabilities:

• P(User) = Prior probability of being a drug user = 0.05
• P(Non-User) = 1 - P(User) = 0.95
• P(Positive|User) = Probability of testing positive if the person is a drug user = 0.65
• P(Positive|Non-User) = Probability of testing positive if the person is not a drug user = 0.03

We use Bayes' theorem to find the posterior probability:

P(User|Positive) = (P(Positive|User) * P(User)) / (P(Positive|User) * P(User) + P(Positive|Non-User) * P(Non-User))

Inserting the numbers, we get:

P(User|Positive) = (0.65 * 0.05) / ((0.65 * 0.05) + (0.03 * 0.95)) = 0.0325 / 0.06085 ≈ 0.533

The posterior probability that the athlete is a drug user given that her test result is positive is approximately 0.533.