Question

task

When asked an embarrassing question in a
survey—such as whether the respondent has
ever shoplifted—individuals may be reluctant
to answer truthfully. However, answers might
be more truthful if the survey incorporates a
random component, such as a coin toss, that
prevents the questioner from determining
whether any given individual is guilty (Warner
1965). For example, consider a survey of a
population in which 20% of individuals really
have shoplifted at least once. The survey
asks every participating individual to begin
by flipping a fair coin twice. If the result of
the first toss is heads, then the individual is
instructed to answer honestly the question “did
the second toss also yield heads?” If the first
coin toss yields tails, however, the respondent is
instructed to answer honestly the question “have
you ever shoplifted?”

a. Draw a probability tree that describes all
possible outcomes of such a survey and their
probabilities.
b. What is the overall probability that a randomly
sampled respondent answers yes?

Answer 1

A)

Consider a survey of a population in which 20% of individuals have shoplifted at least once. Suppose the teacher requested to answer the questions, ' had the second toss also yielded heads? ' And have shoplifted the shoppers ever? ’This is solved using the notion of a distribution of probability.

Part B)

The overall probability is:

P(Yes)=0.25+0.10=0.35​

The overall probability is 0.35

Concept Used :

The concept of probability is used to solve this problem.

Probability is the state or an extent to which a given event is likely to happen. In general, probability is defined as a number between 00 and 11, where 00 implies the impossibility of an event to occur, and 11 implies the certainty.