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

P(IDENTIFIED GENUINE | GENUINE SUBMISSION) = 0.95

So, P( IDENTIFIED COPIED| GENUINE SUBMISSION) = 0.05

P( IDENTIFIED COPIED | COPIED) = 0.8

P( COPIED)= 0.15

P( GENUINE WORK) = 1-0.15 = 0.85

P( COPIED WORK | IDENTIFIED COPIED) =

={ P( COPIED)*  P( IDENTIFIED COPIED | COPIED) } / { P( COPIED)*  P( IDENTIFIED COPIED | COPIED) + P( GENUINE WORK)* P( IDENTIFIED COPIED| GENUINE SUBMISSION) = 0.05}

= { 0.15*0.8} /{ 0.15*0.8 + 0.85*0.05}

=0.7385