In surveys about sensitive topics, respondents are sometimes given ways to “hide” their answers from the surveyor. In a survey of taxpayers, one of the questions is, “Did you cheat on your taxes?” To answer, the respondent is asked to toss a coin. If it lands heads, the respondent must answer “yes.” If it lands tails, the respondent must answer the question truthfully, either “yes” or “no” (the answer has to be the one that is true). Assume that all respondents follow this procedure, and that for 10% of the respondents the truthful answer is “yes.” Also assume that the result of a respondent’s coin toss is independent of whether or not the respondent cheated on his/her taxes.

One of the respondents is picked at random.
1)Given that the respondent cheated on his/her taxes, what is the chance that he/she answered “yes”?
2)Given that the respondent did not cheat on his/her taxes, what is the chance that he/she answered “yes”?
3)Given that the respondent answered “yes,” what is the chance that the respondent cheated on his/her taxes?