Question

suppose that 5% of the general population has a disease and the test for the disease is acurate 80% of the time, what is the probability of testing postive for the disease

Answer 1

Let 5% be 0.05 and 80% be 0.80.

P(testing positive) = 0.05/0.80

You finish.

Answer 2

The probability of testing positive for the disease is 23%.

Explanation:

It is given that 5% of the general population has a disease and the test for the disease is accurate 80% of the time.

A: General population has a disease.
`P(A)=(5)/(100)`

B: General population has no disease.
`P(B)=(95)/(100)`

C: The test for the disease is accurate.
`P(C)=(80)/(100)`

D: The test for the disease is inaccurate.
`P(D)=(20)/(100)`

We have to find the probability of testing positive for the disease. The result is possible if the person has disease and test is accurate or the person has no disease and test is inaccurate.

`P=P(A\cap C)+P(B\cap D)`

`P=P(A)* P(C)+P(B)* P(D)`

`P=(5)/(100)* (80)/(100)+(95)/(100)* (20)/(100)`

`P=0.23`

`P=23\%`

Therefore the probability of testing positive for the disease is 23%.