Probability of a tax claim being bad, given that it is investigated by inspectors

Explain that there are three equivalent sets of probabilities:

The formulae for moving between the 2nd and 3rd of these is called Bayes theorem.

Tax inspectors investigate some of the tax returns that are submitted by individuals if they think that some claims for expenses are too high or are unjustified.

A investigation of the tax return does not always conclude that the claims were fraudulent — their suspicions are rarely 100% accurate.

(The probabilities are not real.)