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.
Draw a two-stage probability tree and use it to answer the following questions.
a. Based on this morning’s machine inspection, how likely is it that the first unit produced is defective?
b. If the first unit is defective, what’s the probability that the machine is in Status A1 . (That is, use the fact that the first unit is defective to revise the 95% probability that the machine is working properly.)