### Working Backward

#### Certainty

One use of decision trees is to sort out options in complex decision situations. The textbook's example has us comparing a number of urban development opportunities — wildlife refuge, mini-golf, park, condos, single family homes, apartments. We group these into two categories: recreation and housing. Then we compare the recreation alternatives, select the best one, and then compare the housing options and select the best one. Then, we compare the top housing option and the top recreation option.

This is called working backward because we start over on the right, assuming we've made some decisions to get us to the last branching point. In effect, we are saying, "assume you have gotten to this point, then what should you do?" This allows us to prune the tree and simplify the decision task.

As the book says, no big deal.

### Uncertainty

Here's the example the book offers:

A hospital administrator-we'll call her Harriet-must let a contract for reseeding the hospital lawn. She can give the contract to company A, which has agreed to do the job for \$1500 provided that the weather is good over the next month; the charge will escalate to \$2400 if the weather is bad . (Bad weather is defined as less than one or more than four inches of rain.) Or she can give it to company B, which has submitted a tlat bid of \$2000. Meteorological records indicate that there is a 15 percent chance there will be less than one inch of rain and a 25 percent chance of more than four inches. Thus there is a 60 percent chance that the weather will be good. What should Harriet do?

Sketch the decision tree.