Question

A company administers a drug test to its employees. Use

the two-way table to answer the question that follows.
Total
Employee Test Results
Employee Employee
Uses is Drug
Drugs
Free
Test Positive for
20
12
Drug Use
Test Negative for
0
468
Drug Use
Total
20
480
IN
32
468
500
If a test is positive, what is the probability, written
as a percent, that the employee is guilty? If
necessary, round your answer to the nearest
percent.

Answer 1

`Pr = 62.5\%`

Explanation:

Given

See attachment for table

Required

Probability that the selected employee uses drug, if the test is positive

From the attached table,

`n(Positive) = 32` --- Positive for drug

`n(Positive\ and\ Uses\ Drugs) = 20`

So, the required probability is calculated using:

`Pr = (n(Positive\ and\ Uses\ Drugs))/(n(Positive))`

`Pr = (20)/(32)`

`Pr = 0.625`

Express as percentage

`Pr = 0.625 * 100\%`

`Pr = 62.5\%`