Question

5. ‘Round about 10% of Americans have diabetes. You take a test for diabetes that’s 95% accurate.

5a. The test returns a positive result -it says you have the diabetus. What’s the probability that you don’t actually have diabetes?

5b. The test returns a negative result. What’s the probability that you actually do have diabetes?

5c. Say the test is 99% accurate instead. Redo parts (a) and (b).

Answer 1

a)

P(don't have disease | positive test result) = P(don't have disease and positive test result)/ P(positive test result)

= 0.9 * 0.05/(0.9 * 0.05 + 0.1* 0.95)

= 0.32142

b)

P(have disease | negative test result)

= P(have disease and negative test result) /P(negative test result)

= 0.1 * 0.05 / (0.1*0.05 + 0.9 * 0.95)

= 0.0058139

c)

if 99% accuracy

then a) would be 0.9 * 0.01/(0.9 * 0.01 + 0.1* 0.99) = 0.0833

b) would be 0.1 * 0.01 / (0.1*0.01 + 0.9 * 0.99) = 0.001121