We have two questions. Question1 is sensitive: Do you smoke marijuana? Question

Question

We have two questions. Question1 is sensitive: Do you smoke marijuana? Question 2 is innocuous: Does your telephone number end with an even digit? Then we ask the respondent to toss a coin and answer Q1 correctly if head turns up, and answer Q2 correctly if tail turns up. The investigator does not know which question the respondent is answering and the secrecy of information is maintained. From such responses, find P(people in survey smoke marijuana), which is the true proportion of individuals smoking marijuana. (The answer is not simply 50%. )

Explanation / Answer

well as we are saying that  we ask the respondent to toss a coin and answer Q1 correctly if head turns up, and answer Q2 correctly if tail turns up

so that means that as we know the probability of toss a coin (0.5)

then we will have a probability of true proportion of individuals smoking maijuana by looking the probabilty of the coin

P(people in survey smoke marijuana), which is the true proportion of individuals smoking marijuana.

is 0.50 = 50%

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