Question

Suppose that 5% of the general population has a disease and the test for the disease is accurate 80% of the time. What is the probability of testing positive for the disease?

Answer 1

Explanation:

Say we are testing 100 people

we test 100 times

80 of the 100 tests result in 5 people having the disease.

so 5 people of 80 of 100 test have this disease

therefore, 5/80/100

.065

Answer 2

The probability of testing positive for the disease is:

23%

Explanation:

The population who have disease = 5%

Hence, the population who do not have disease= 95%

( since 100%-55=95%)

Also, the percent that the test is accurate= 80%

and the percent that the test is not accurate= 100%-80%=20%

Hence, the probability of testing positive for the disease is :

The person actually has disease×Test is positive+Person do not have disease×test is not accurate

= 0.05×0.80+0.95×0.20

= 0.23

Hence, the probability is: 23%