1. Chance Nodes:

- compute EMV (estimated monetary value) which is the weighted average of outcomes which is the sum of expected values (EV) of branches
- EV = Σ
_{i}= P_{i}V_{i}where P = probability of*i*and V=value of outcome branch*i*

- EV = Σ

2. Choice Nodes: select best branch

Test Branches

1. With testing we get a 3 branch tree

2. At the end we compare test branch value - test to the no-test branch

3. This tells us the value of information

# Q.95

You never know what the weather is going to be around here. Some days you need a hat and some days you need a scarf. The smart person, hey say, always brings both. But suppose there is a definite hassle involved in bringing either (e.g., you ride a bike and space is tight). Sketch a decision tree that takes into account a cost to bringing either and a cost to not having either and cost to not having either when you need them and the possibility that on a given day you might need one, the other or both. Use plausible numbers for your own choices.

What if we had a crystal ball and definitely know the weather?

P(windy)=0.7 P(not windy)=0.3 but if the crystal ball says it will not be windy it will not be so:

# Q.93

**Q93.** A new device at your favorite big box store costs $200. It has a one year guarantee from the manufacturer. The cashier offers you a special deal on a three year replacement warranty (assume it's good, will be honored, etc.) — $40. You estimate that the chances of the device failing during second and third years is 25% and that the price of replacement by then will be $150. Should you buy the service plan? What are the parameters of this decision model?