A 2013 Sage North America survey examined the “financial literacy” of small business owners. The study found that 23% of small business owners indicated concern about income tax compliance for their business; 41% of small business owners use accounting software, given that the small business owner indicated concern about income tax compliance for his or her business. Given that a small business owner did not indicate concern about income tax compliance for his or her business, 58% of small business owners use accounting software. (Data extracted from “ Sage Financial Capability Survey: What Small Business Owners Don’t Understand Could Be Holding Them Back,” April 17, 2013, bit.ly/Z3FAqx.)
a. Use Bayes’ theorem to find the probability that a small business owner uses accounting software, given that the small business owner indicated concern about income tax compliance for his or her business.
b. Compare the result in (a) to the probability that a small business owner uses accounting software and comment on whether small business owners who are concerned about income tax compliance for their business are generally more likely to use accounting software than small business owners who are not concerned about income tax compliance for their business.