Professors often attempt to determine if the submissions by the students are genuine or copied off the web sources. The program that performs this task is only 95 % accurate in correctly identifying a genuine submission and 80% accurate in correctly identifying copies. Based on the past statistics, 15% of the student turned in copied work. If a work is identified as a copy by the program, what is the probability that it is indeed a sample of copied work.

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joaobezerra joaobezerra · Answer 1 · 2021-04-23T02:46:52+02:00

Answer:

0.7385 = 73.85% probability that it is indeed a sample of copied work.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Identified as a copy

Event B: Is a copy

Probability of being identified as a copy:

80% of 15%(copy)

100 - 95 = 5% of 100 - 15 = 85%(not a copy). So

[tex]P(A) = 0.8*0.15 + 0.05*0.85 = 0.1625[/tex]

Probability of being identified as a copy and being a copy.

80% of 15%. So

[tex]P(A \cap B) = 0.8*0.15 = 0.12[/tex]

What is the probability that it is indeed a sample of copied work?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.12}{0.1625} = 0.7385[/tex]

0.7385 = 73.85% probability that it is indeed a sample of copied work.