Question

Here is a scenario that came up in the nationally syndicated column called "Ask Marilyn" in Parade Magazine. Suppose a certain drug test is 95% accurate, meaning that if a person is a user, the result is positive 95% of the time, and if she or he isn't a user, it's negative 95% of the time. Assume that 5% of all people are drug users.

Assume that the population is 10,000, and fill in the accompanying table (9 answers total)
Drug user Not a drug user Totals
Test positive
Test negative
Totals

Answer 1

Drug User Not a drug user Totals

Test positive 475 475 950

Test negative 25 9025 9050

Totals 500 9500 10,000

Explanation:

Drug User Not a drug user Totals

Test positive 475 475 950

Test negative 25 9025 9050

Totals 500 9500 10,000

As we know that 5% of all people are drug users

Total drug users=5% of 10,000=0.05(10,000)=500

Total non drug users= Total people - drug users= 10,000-500=9500

or total non drug users=95% of 10,000=0.95(10,000)=9500

Test is correct for 95% of times means that 95% times drug users test results is positive and non drug users test results is negative.

Test positive for drug user= 95% of 500=0.95(500)=475

Test negative for non drug user= 95% of 500 = 0.95(9500)=9025

Test is correct for 95% of times and it means that 5% of times test is not correct. It means that 5% of times drug users test results is negative and non drug users test results is positive.

Test negative for drug user= 5% of 500=0.05(500)=25

Test positive for non drug user= 5% of 9500 = 0.05(9500)=475