n order to determine the proportion of students who have cheated on a test at le

Question

n order to determine the proportion of students who have cheated on a test

at least once in the past year, we conducted a survey among students. Since cheating

is a ”sensitive” subject, we had to use a type of survey that would respect students’

privacy.

In the interview process for each student, the student flips a coin, hidden from the

interviewer. If the coin lands heads, the student answers “yes”. If the coin lands tails,

the student answers truthfully to the question. This way, the interviewers does not know

if a “yes” was the result of a guilty plea.

Suppose the total number surveyed was 40 students, and 25 of them gave a ”yes” re-

sponse, find the probability of cheating

Problem 2: Iorder to determine the proportion of students who have chcated on a test at least once in the past year, we conducted a survey among students. Since chcating is a "sensitive" subject, we had to use a type of survey that would respect students' privacy In the interview process for cach student, the student flips a coin, hidden from the interviewer. If the coin lands heads, the student answers "yes". If the coin lands tails, the student answers truthfully to the question. This way, the interviewers does not know if a "yes" was the result of a guilty plea. Suppose the total number surveyed was 40 students, and 25 of them gave a "yes" re- sponse, find the probability of cheating.

Explanation / Answer

Total surveyed students = 40

Total yes's = 25

Total no's = 15

Lets thier are X number of heads out of 40 coin toss that means all of these X will say yes. Rest ( 40 - X) students had tail in their coin toss so out of these (40 -X), if the probability of cheaters are p, then (40-X)p will say yes.

So

X + p (40 -X) = 25

p = (25 -X)/ (40 -X)

so if we take expected value of X, which is 20.

p = (25 - 20)/ (40 - 20) = 0.25

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