Discuss the following:
Q: Suppose that four inspectors at a film factory are suppose to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages. Tom, who stamps 60% of the packages, fails to stamp the expiration date once in every 100 packages. Jeff, who stamps 15% of the packages, fails to stamp the expiration date once in every 90 packages. And, Pat, who stamps the remaining packages, fails to stamp the expiration date once in every 200 packages. If a customer complains that her package of film does not show the expiration date, what is the probability that it was inspected by John?