More Embarrassing Questions

For a statistical study, you need to figure out what proportion of people have a certain private attribute. But the attribute being private, no body really wants to tell you.

So, you devise the following protocol:

  1. You ask the subject to toss a fair coin. They do not show you the result of the toss.
  2. On Heads, they tell you their truthful answer.
  3. On Tails, they toss the coin again and
    • On a Heads, they tell Yes
    • On a second Tails, they tell No

If in a sample of 100 people, 30 people tell you Yes, then what is the expected number of people who really have the private attribute?

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