Embarassing Question

For a study, you need to know what percentage of people do a certain private thing. But the thing being private, they are really unwilling to tell you about it.

So, you device the following protocol:

  1. The subject tosses a fair coin. (But the subject does not show you the result of the coin toss.)
  2. If Heads show up, you say Yes.
  3. If Tails show up, you answer truthfully.

After running this experiment on about 100 people, you observe that about 15 people tell you No.

What is the expected number of people who really do not do the private thing?

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