Expert: Sherry Wallin - 12/25/2009

Question
Setswana Nosks estimates that the probability its lathe tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. If the lathe is out of adjustment, howeever, the probability of a good part being produced is only 0.2. A part randomly chosen is inspected and found to be acceptable. What is the posterior probability that lathe tool is properly adjusted?

This is what I have so far:
P(adjusted)= .50     P(out of adjustment)=.50
P (.08|adjusted)       P(.08|out of adjustment)


Answer
Hi Liza, I am not sure where you got your numbers. P(adjusted) = .8 which means the probability it is not adjusted is .2. You want the probability that given a part passes inspection that the tool was properly adjusted. Also from the problem statement you know that the probability that a part will pass inspection given the lathe is out of adjustment is .1. Maybe this will help you solve the problem?

Math Prof