Question 4.88

4.88 Examined by the IRS.

The IRS examines (audits) some tax returns in greater detail to verify that the tax reported is correct. The rates of examination vary depending on the size of the individual's adjusted gross income. In 2014, the IRS reported the percentages of total returns by adjusted gross income categories and the examination coverage (%) of returns within the given income category:21

209

Income ($) Returns filed (%) Examination
coverage (%)
None 2.08 6.04
1 under 25K 39.91 1.00
25K under 50K 23.55 0.62
50K under 75K 13.02 0.60
75K under 100K 8.12 0.58
100K under 200K 10.10 0.77
200K under 500K 2.60 2.06
500K under 1MM 0.41 3.79
1MM under 5MM 0.19 9.02
5MM under 10MM 0.01 15.98
10MM or more 0.01 24.16
  1. Suppose a 2013 return is randomly selected and it was examined by the IRS. Use Bayes's rule to determine the probability that the individual's adjusted gross income falls in the range of $5 to $10 million. Compute the probability to at least the thousandths place.
  2. The IRS reports that 0.96% of all returns are examined. With the information provided, show how you can arrive at this reported percent.