# Posterior probability

Ace Machine Works 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, however, the probability of a good part being produced is only 0.2. A part randomly chosen is inspected and found to be acceptable. At this point what is the posterior probability that the lathe tool is properly adjusted?

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#### Solution Preview

probability that the lathe is properly adjusted= 0.8

Therefore the probability that the lathe is not properly adjusted=1-0.8= 0.2

the probabilty that the parts are acceptable when the lathe is properly adjusted = 0.9

the probabilty that the parts are acceptable when the lathe is not ...

#### Solution Summary

Calculates the posterior probability that the lathe tool is properly adjusted.