Please solve this probability question and provide the explanation.

The IRS would like to find out the proportion of Americans who lie on their taxes. They select a random sample (e.g. by tax file numbers) of Americans and ask them if they have ever lied on their taxes. Of course, they promise that there will be no consequences if the answer is 'yes', and that they will not record this information against the taxpayer's identity. If you had cheated on a tax return previously, would you answer truthfully? Your answer is probably 'No', because you wouldn't trust the IRS not to use your answer against you. In this task, you'll look at a method with which an individual can safely disclose this information. Procedure: 1. The respondent secretly flips a coin twice. 2. If the first flip shows 'heads', they are to answer truthfully. 3. Otherwise, they are to answer 'yes' or 'no' according to the second flip being 'heads' or 'tails'. The idea is that this way, even if they answer 'yes', IRS can't prove that they did it because they cheated rather than because the coin told them to, and vice versa. Below, 0 the (unknown) true proportion of tax return frauds are D