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Human error is the most common kind

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.]


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