Suppose we are interested in the condition of a machine that produces a particular item. Let A designate the event "the machine is in good working condition". Let B be the event "the machine is not in good owrking condition". We know from experience that P(A)= 0.90. Further, let C be the event "a defective item is produced". We also know from experience that a defective item is produced from a machine in good operating condition only 1% of the time, while 10% of the time the item is defective if the machine is not in good operationg condition.
-What is the value of P(C|A)?
-What is the value of P(C|B)?
-What is the value of P(B)?
-What is the P(C)?
-Suppose you are givien that an item is defective. What is the probability the defective item was produced by a machine in good operating condition?