In a meat packaging plant, Machine A accounts for 60% of the plant's output while Machine B accounts for 40% of the plant's output. 1% of the packages from Machine A are improperly sealed while 2% of the packages from Machine B are improperly sealed.
a) What is the probability that a randomly chosen package is improperly sealed?
b) If a package is selected at random and found to be improperly sealed, what is the probability that it came from Machine A?
c) If a package is selected at random and found to be properly sealed, what is the probability that is came from Machine A?