Business statistics

Question

A certain disease has an incidence rate of 0.7%. If the false negative rate is 5% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease.

   

Give your answer accurate to at least 3 decimal places

Answer 1

I agree with Raymond's method; conditional probability questions are often easiest to understand if you represent the probabilities as frequencies over some large set of people.

I want to point out that Raymond made a minor reading error: The incidence is .7%, not 70%. This changes the answer a bit! Maybe you can try to follow his method with the corrected incidence plugged in. If you have 100 people, how many will have the disease? Not 70; something 100 times smaller than that. Actually, you might prefer to consider a larger set of people--like a million--because then you will avoid having fractions of people. Mathematically, this doesn't change anything, but it might make the numbers easier to intuit.

If there really is a disease with a 70% incidence rate, hopefully it's pretty minor!

Answer 2

70% have the disease

5% false negative

2% false positive

100 people

+ - total

D 66.5 3.5 70

~D .6 29.4 30

total 67.1 32.9 100

P(+)=.67.1

P(D/+)= 66.5/67.1 =99.106%

= probability of disease if positive test