It is known from historical data that 6% of all income tax
returns for self-employed individuals are fraudulent.
Fraudulent returns are very likely to contain a deduction
for a home office. Specifically, 70% of fraudulent returns
contain this deduction, whereas only 40% of honest
(nonfraudulent) returns contain this deduction. A
self-employed individual's tax return is randomly selected
and it contains a home office deduction. How likely is it
that this return is in fact fraudulent?