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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?

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?

check_circleAnswer
Step 1

Given data
The response is always yes when tail occurs
Making tree diagram as per the question

Plagiarized
always yes
0.5
0.5
Tail
Plagiarized
0.3
Yes
Head
0.5
0.7
Plagiarized No
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Image Transcriptionclose

Plagiarized always yes 0.5 0.5 Tail Plagiarized 0.3 Yes Head 0.5 0.7 Plagiarized No

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Step 2

conditional probability that a randomly chosen student who answers ...

0.3 x 0.5
= 0.375
0.3 x 0.50.5 x 0.5
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Image Transcriptionclose

0.3 x 0.5 = 0.375 0.3 x 0.50.5 x 0.5

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Probability

Basic Probability

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