Fraudulent tax claims
Use this diagram to explain that there is no contradiction between the following:
pbad claim | investigated = 0.471
pinvestigated | bad claim = 0.8
The two halves of the diagram show the different sets of marginal and conditional probs.
The slider adjusts the marginal proportion of the population making fraudulent tax claims, keeping the characteristics of the actual investigation constant — e.g. P(investigated given bad claim) stays 0.8.
Drag the slider and observe that the greater P(bad claim), the greater P(bad claim given investigated) and P(bad claim given not investigated).
Although the proportion of bad claims that are investigated stays 0.8, P(bad claim given investigated) could potentially be any value.
Medical diagnostic tests for a disease are rarely 100% accurate. There are two types of error:
The probabilities are not for a real disease or diagnostic test.