Question

Consider conditional probability and discrete math. Please provide a full and correct solution. A large company gives a new employee a drug test. The False-Positive rate is 4% and the False-Negative rate is 5%. In addition, 1% of the population uses the drug. What is the probability that a new employee tests positive for the drug?

Answer 1

To find the probability that a new employee tests positive for the drug, we need to consider the different scenarios that could lead to a positive test result. The probability of testing positive is 0.0492, or 4.92%.

Step-by-step explanation:

To find the probability that a new employee tests positive for the drug, we need to consider the different scenarios that could lead to a positive test result. There are two possibilities: either the employee uses the drug and tests positive (True Positive), or the employee doesn't use the drug but tests positive incorrectly (False Positive).

Let's calculate the probability of each scenario:

Probability of the employee using the drug (P(Drug)) = 0.01

Probability of the employee not using the drug (P(No Drug)) = 1 - P(Drug) = 0.99

Probability of a False Positive (P(FP)) = 0.04

Probability of a True Positive (P(TP)) = 1 - P(FP) = 1 - 0.04 = 0.96

Now we can calculate the probability of testing positive (P(Positive)):

P(Positive) = P(Drug) * P(TP) + P(No Drug) * P(FP) = 0.01 * 0.96 + 0.99 * 0.04 = 0.0096 + 0.0396 = 0.0492

Therefore, the probability that a new employee tests positive for the drug is 0.0492, or 4.92%.