Decision Trees - Bayes Rule Example

In this video you will see an example of finding posterior probabilities based on given information.
This example is from the following textbook:
Wayne L. Winston (2004), Operations Research: Applications and Algorithms, 4th Edition

[@Whatdoyouwant1211]

sorry, i hope u reply. Yes we should pick a smaller expected value. So -1600 is smaller than -1575 right ???

[@ISE_Post]

We always pick the largest value (-1,575 > -1,600). In cases where the values represent cost, which is the case here, it implies less inspection cost over time. If the values represent profit, we will see positive values and larger values mean more profit. So always pick the largest value when you want to maximize the expected value of a decision tree. Also, remember, this is not for a one time decision. It is for setting policies because the decision will be applied to many many inspection cases and we want the average cost per inspection to be as low as possible.