Question

A ChatGPT detector is used to detect if one assignment is totally written by ChatGPT, instead of students. Suppose that the ChatGPT detector can detect 75% of GPT-written assignments, but incorrectly identifies 10% of student-written assignments as GPT-written assignments. A university believes that 95% of its students will complete their assignments by themselves rather than by using ChatGPT. (a) What is the probability of the event A = {An assignment chosen at random is written by a student}? (b) What is the probability of the event B = {An assignment is detected to be a GPT-written assignment}? (c) What is the probability that an assignment that is detected to be a GPT-written as- signment is actually written by a student? Hint: use the events A and B defined above

          A ChatGPT detector is used to detect if one assignment is totally written by ChatGPT, instead
of students. Suppose that the ChatGPT detector can detect 75% of GPT-written assignments,
but incorrectly identifies 10% of student-written assignments as GPT-written assignments. A
university believes that 95% of its students will complete their assignments by themselves rather
than by using ChatGPT.
(a) What is the probability of the event
A = {An assignment chosen at random is written by a student}?
(b) What is the probability of the event
B = {An assignment is detected to be a GPT-written assignment}?
(c) What is the probability that an assignment that is detected to be a GPT-written as-
signment is actually written by a student?
Hint: use the events A and B defined above

Added by Ryan B.

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