Question

Cheating on Your Taxes?

Suppose 5% of all people filing the long income tax form seek deductions that they know are illegal, and an additional 2% incorrectly list deductions because they are unfamiliar with income tax regulations. Of the 5% who are guilty of cheating, 80% will deny knowledge of the error if confronted by an investigator. If the filer of the long form is confronted with an unwarranted deduction and he or she denies the knowledge of the error, what is the probability that he or she is guilty?

Answer 1

Let x=illigeal deduction filed

y=knowledge of error is denied

from given data we get

P(x)=0.05/0.07=0.7142

P(y)=80%=0.8

and prob that person who is not guilty would definetly denied the knowldege

P(y|x')=1

Calculating Probability that the event illigeal deduction filed given that the event of knowledge of error is denied

P(x|y)=

Using Bayes rule :

Probabilty that he or she guilty is 2/3