Drug usage in the workplace costs employers incredible amounts of money each year. drug testing potential employees has become so prevalent that drug users are finding it extremely hard to find jobs. drug tests, however, are not completely reliable. the most common test used to detect drugs is approximately 97% accurate. to decrease the likelihood of making an error, all potential employees are screened through two tests, which are independent, and each has 95% accuracy. if a potential employee were drug free, what is the probability that the person would pass the first test and fail the second test?

Question

Jayson Scott

Business

24 March, 21:01

Drug usage in the workplace costs employers incredible amounts of money each year. drug testing potential employees has become so prevalent that drug users are finding it extremely hard to find jobs. drug tests, however, are not completely reliable. the most common test used to detect drugs is approximately 97% accurate. to decrease the likelihood of making an error, all potential employees are screened through two tests, which are independent, and each has 95% accuracy. if a potential employee were drug free, what is the probability that the person would pass the first test and fail the second test?

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Rylie Suarez · Answer 1

The employee takes the first test, with 95% accuracy. If he’s drug free, he has 95% probability to pass the test. 95% = 95/100 = 0.95

Then the employee takes the second test, also with 95% accuracy. If he’s drug free, he has 5% probability to fail the test. 5%=5/100=0.05

Joint probability is calculated like this: probability 1*probability 2.

In this case, joint probability = 0.95*0.05 = 0.0475

which means 4,75%