You work as a tax auditor at the , searching through business tax returns for evidence of tax evasion. You are particularly perceptive and diligent and can detect the presence of tax evasion in 94% of cases where it has occurred. Unfortunately, in your enthusiasm you occasionally also report there has been tax evasion when in fact there was none - your tendency is to report 4% of valid tax returns as containing evasion. Overall 2% of businesses actually evade some tax*. (* made up statistic to use for this tutorial!)

1. You are randomly allocated a business to audit and conclude that their return shows signs of tax evasion. Based on your decision, what is the probability the business has actually been evading their taxes?

2. The next day you are given another randomly chosen business, and this time conclude they are clear of tax evasion. Based on your decision, what is the probability the business has actually been evading their taxes?(ctd...)

3.ATO 4 Your colleague in the audit department, Thelonious Monkey, is not as well trained as you and gets distracted by and generally monkeying around. As a result he only detects tax evasion in 70% of the tax returns in which it is present, while passing as valid 99% of tax returns in which there is no evasion. Recalculate questions 1 and 2 for Thelonious.