Sampling and Experiments · Superchallenge problem

To ask about cheating on taxes, each respondent privately draws a card. With probability $\dfrac{3}{4}$ the card says "Answer: I have cheated on my taxes. True or false?" and with probability $\dfrac{1}{4}$ it says "Answer: I have NEVER cheated on my taxes. True or false?" The interviewer only hears "true" or "false", never which card was drawn. If $40\%$ of all answers are "true", what percent of the population would you estimate has cheated? (Assume everyone answers honestly.)