Question

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.

Answer 1

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

Explanation:

Conditional Probability

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

`P(B|A) = (P(A \cap B))/(P(A))`

In which

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

`P(A \cap B)` 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

`P(A) = 0.8*0.15 + 0.05*0.85 = 0.1625`

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

80% of 15%. So

`P(A \cap B) = 0.8*0.15 = 0.12`

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

`P(B|A) = (P(A \cap B))/(P(A)) = (0.12)/(0.1625) = 0.7385`

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