Question

We ask each student being surveyed to toss a coin in private. If the coin lands "heads," they are to answer the question, "Have you plagiarized a term paper?" truthfully. If the coin lands "tails," they are told always to answer "yes," whether they have in fact plagiarized or not. Imagine that the true fraction of students who have plagiarized is in fact 0.3, and imagine that participants in the survey indeed follow the randomized response procedure accurately and honestly. What is the conditional probability that a randomly chosen student who answers "yes" to the survey has in fact plagiarized

Answer 1

Conditional probability of a student, who has actually plagiarized, answering "yes" to the survey is 0.375.

Step-by-step explanation:

This is easily explanined if we first take the probability of each answer (yes / no) depending on what they fet flipping the coin.

• Tails [always yes] = 0.5 -> Plagiarism = 0.5
• Heads [yes or no] = 0.5 > Two option: (1) True Plagiarism = 0.3; (2) False Pagiarism = 0.7

Now, what we have to do is multiply the "yes" answers from both possible coin tosses (0.5 x 0.3) and divide them by the rest of probable answers (0.5, 0.5, 0.5 & 0.3).

Better expressed like this:

0. 5 x 0.3 / 0.3x0.5+0.5x0.5 = 0.375