Editing Base rate fallacy (section)

===Example 1: Disease===
==== High-prevalence population ====
{| class="wikitable floatright" style="text-align:right;"
! Number<br />of people !! Infected !! Uninfected !! Total
|-
! Test<br />positive
| 400<br />(true positive) || 30<br />(false positive)
| 430
|-
! Test<br />negative
| 0<br />(false negative) || 570<br />(true negative)
| 570
|-
! Total 
| 400 || 600 
! 1000
|}
Imagine running an infectious disease test on a population ''A'' of 1,000 persons, of which 40% are infected. The test has a false positive rate of 5% (0.05) and a false negative rate of zero. The [[expected value|expected outcome]] of the 1,000 tests on population ''A'' would be:

{{block indent|Infected and test indicates disease ([[true positive]])
{{block indent|1=1000 × {{sfrac|40|100}} = 400 people would receive a true positive}}}}
{{block indent|Uninfected and test indicates disease (false positive)
{{block indent|1=1000 × {{sfrac|100 – 40|100}} × 0.05 = 30 people would receive a false positive}}
The remaining 570 tests are correctly negative.}}

So, in population ''A'', a person receiving a positive test could be over 93% confident ({{sfrac|400|30 + 400}}) that it correctly indicates infection.

====Low-prevalence population====
{| class="wikitable floatright" style="text-align:right;"
! Number<br />of people !! Infected !! Uninfected !! Total
|-
! Test<br />positive
| 20<br />(true positive) || 49<br />(false positive)
| 69
|-
! Test<br />negative
| 0<br />(false negative) || 931<br />(true negative)
| 931
|-
! Total 
| 20 || 980 
! 1000
|}
Now consider the same test applied to population ''B'', of which only 2% are infected. The expected outcome of 1000 tests on population ''B'' would be:

{{block indent|Infected and test indicates disease (true positive)
{{block indent|1=1000 × {{sfrac|2|100}} = 20 people would receive a true positive}}}}
{{block indent|Uninfected and test indicates disease (false positive)
{{block indent|1=1000 × {{sfrac|100 – 2|100}} × 0.05 = 49 people would receive a false positive}}
The remaining 931 tests are correctly negative.}}

In population ''B'', only 20 of the 69 total people with a positive test result are actually infected. So, the probability of actually being infected after one is told that one is infected is only 29% ({{sfrac|20|20 + 49}}) for a test that otherwise appears to be "95% accurate".

A tester with experience of group ''A'' might find it a paradox that in group ''B'', a result that had usually correctly indicated infection is now usually a false positive. The confusion of the [[posterior probability]] of infection with the [[prior probability]] of receiving a false positive is a natural [[fallacy|error]] after receiving a health-threatening test result.