Refer to Exercise 43. Suppose the first unit is defective. Use Bayes’ theorem to determine the probability that the machine is in Status A1.
In Exercise 43
When a metal stamping machine is working properly (call it Status A1) only 2% of the units it produces are defective. When it slips out of adjustment (call it Status A2) the defective rate jumps to 20% and the machine has to be shut down and adjusted. Each morning you do a visual inspection of the machine before beginning production and judge its condition based on your inspection. Today, based on your visual inspection, you judge that it’s 95% likely that the machine is fine (Status A1) and only 5% likely that it’s out of adjustment (Status A2). You now turn on the machine and produce the first unit.