# Thread: Disease infection - simple probability

1. ## Disease infection - simple probability

A disease is known to exist in 3.5% of a population. A test is 90% effective in detecting the disease, but has a 5% error-rate for "false" positive detection (an uninfected person tests positive). If the test is given to the entire population, what percent of the population would test:

A. Positive for the disease

B. Correctly

2. Originally Posted by MathGeezer
A disease is known to exist in 3.5% of a population. A test is 90% effective in detecting the disease, but has a 5% error-rate for "false" positive detection (an uninfected person tests positive). If the test is given to the entire population, what percent of the population would test:

A. Positive for the disease

B. Correctly
In the chart below D means 'disease' and ND means 'no disease'.

---> Positive 5% = 0.05*0.965 Branch 1
---> ND (96.5%)
---> Negative 95% = 0.95*.965 Branch 2

Population
---> Positive 90% = 0.90*0.035 Branch 3
---> D 3.5%
--->Negative 10% = 0.10 * 0.035 Branch 4

A. Add branches 1 and 3, convert the number to percentage.
B. Add branches 2 and 3, convert the number to percentage.