It is difficult to conduct sample surveys on sensitive issues because many people will not answer questions if the answers might embarrass them. Randomized response is an effective way to guarantee anonymity while collecting information on topics such as student cheating or sexual behavior. Here is the idea. To ask a sample of students whether they have copied a term paper while in college, have each student toss a coin in private. If they coin toss result is heads and they have not copiedd, they are to answer "no." Otherwise, they are to answer "yes." Only the student knows whether the answer reflects the truth or the coin toss, but researchers can use a proper random sample will follow-up for non-response and other good sampling practices.

Suppose that in fact the probability is 0.3 that a randomly chosen student has copied a paper. Draw a tree diagram in which the first stage is tossing the coin and the second is about copying. The outcome at the end of each branch is the answer given to randomized-response question. What is the probability of a "no" answer in the randomized-response poll? If the probability of plagiarism were 0.2, what would be the probability of a "no" response on the poll? Now suppose that you get a 39% "no" answers in a randomized-response poll of a large sample of students in UMD. What do you estimate to be the percent of the population who have plagiarized a paper?