Finite Math, Probabilities

Question

It is believed that 10% of the population has diabetes. A medical firm has a test to detect diabetes. The test shows a positive result (the person has diabetes) in 98% of the cases, however, it will also show a positive results for 1% who are tested and do not have the diabetes (false positive). What is the probability that a person who test positive actually has diabetes?

Answer 1

Draw a two way table.

Population has diabetes Test positive Test negative

Yes 0.10 0.98 x 0.10 0.02 x 0.10

No 0.90 0.01 x 0.90 0.99 x 0.90

So chance that someone who tests positive has diabetes is ( 0.98 x 0.10 / (0.98 x 0.10 + 0.01 x 0.90))