Surveying class cheaters

Suppose you're working with a university trying to determine the number of students who cheated in a given class. Since you can't simply ask students whether or not they cheated (and expect to receive honest answers, even if you promise the survey is anonymous) you and the university have developed the following algorithm that will help determine what proportion of students cheated while retaining anonymity:

• Each student privately flips a coin before being asked if they cheated in class

• If the coin comes up heads, the student will answer honestly

• If the coin comes up tails, the student will flip the coin once more, responding that "yes" they did cheat if it lands heads and that "no" they didn't cheat if it lands tails

• The student will now have privacy, and the researchers should receive honest answers

Given this algorithm, suppose your professor surveyed 1000 students and 410 responded "Yes" that they did cheat in the class. Write a model that will produce the expected range of true cheaters out of the 1000 surveyed. Note that this question is more open-ended, so stating your assumptions and walking through your logic will be more important than your absolute answer.