Permanent Memories has three employess who burn Blu-ray discs. Employee 1 has a 0.002 chance of making an error, employee 2 has a 0.001 chance of making an error, and employee 3 has a 0.004 chance of making an error. The employees burn roughly the same number of discs in a day.
(a) What is the probability that a randomly chosen disc has an error on it?
(b) Given that a disc has an error, what is the probability that employee 1 was the culprit?
(c) Given that a disc has an error and employee 3 was on vacation the day it was burned, what is the probability that employee 2 was the culprit?
[Author Mark Huber. Licensed under Creative Commons.]