Question

Answer the following questions by construct a two-way table.

Suppose that Walmart requires a mandatory drug test for all employees. Walmart is switching to a new test to identify users of cocaine and related illegal drugs. This test is less accurate but cheaper. If a person has used cocaine recently, the test will be positive 85% of the time. But some prescription drugs can also return a positive test result without the use of cocaine. Suppose that this happens 5% of the time. Let’s assume that 3% of the employees are cocaine users. Use this information to answer the following two questions.

a)If the drug test is positive, what is the probability that the test is wrong and the employee is not using cocaine (or a related illegal drug)?

b)If the test is negative, what is the probability that the test is wrong and the employee is using cocaine (or a related illegal drug)?

Answer 1

Given that  that 3% of the employees are cocaine users. The test will be positive 85% of the time when cocaine is used.  The test will be positive 5% of the time when cocaine is not used.

Let us define the events , . The given probabilities are

Using total probability theorem,

A two way table is constructed as given below.

			0.03
			0.97
	0.074	0.926	1.0

a) The probability that the test is wrong and the employee is not using cocaine given the test is positive is a conditional probability.

The conditional probability,

b) The probability that the test is wrong and the employee is using cocaine given the test is negative is a conditional probability.

The conditional probability,