## Lab: Decision Analysis with Probabilistic Information

## Question 1

Ravix Financial Partnerns estimates (subjectively) that the probability its spam filter is properly configured is 0.8. When the spam filter is properly configured, there is a 90% chance that a spam message is being filtered out. If the spam filter configuration is out of date and needs to be configured, the probability of a spam message getting filtered out drops to 20%. Janelle randomly inspects a message in her junk folder (folder where spam messages get filtered to) and finds that it is spam. What is the proability that the spam filter is up-to-date and configured properly is?

## Question 2

An airport uses a security system based on biometrics that has a 99% chance of detecting a terrorist in its database. But, there's a 2% chance that it can falsely flag a person as a terrorist. If 1 in 100,000 people is presumed to be a terrorist based on FBI crime data, then what is the probability that a person setting off an alarm is actually a terrorist?

*Answer*: P(Terrorist | Set off Alarm) = 0.0005## Question 3

- 1% of women at age 40 who participate in routine screening have breast cancer.
- 80% of women with breast cancer will get positive mammograms.
- 9.6% of women without breast cancer will also get positive mammograms.

*Answer*: P(Cancer | Positive Mamogram) = 0.083

## Question 4

Tracy is trying to decide whether to keep her 2014 BMW X1 with 59,688 miles or buy a new Toyota Corolla for her ride-sharing business. She believes she can get $12,800 for her BMW as it is in good condition. However, she wants to sell it and move on to a new car because the car was partially submerged in salt water after a storm flood at her condo building. Her mechanic told her that there is a likelihood of significant repairs necessary over the next few years. She's thinking of getting a Toyota Corolla instead. She has been looking at new cars and the car she wants would cost $18,290. She wants to finance the rest after applying the money from her trade. Sales tax is 8.25% of any cost above her trade-in. Annual insurance costs are about the same for the two cars. She's evaluating whether to finance over 3, 4, or 5 years. She's gotten interest rate quotes for loans of 2.99% for three years, 4.99% for four years, and 5.99% for five years. She does not believe there would be any repair costs for at least four years. After that she thinks that it would be no more than $1000 per year. For the first four years, all routine maintenance is covered by Toyota. The BMW is a different story: there's almost no chance that there wouldn't be repairs. The repair probabilities and costs are as follows:

What is the right decision to make in terms of buyint the Toyota or keeping the BMW and over how many years to finance? Build a decision tree to determine the rational decision.

## Question 5

Farm Grown LLC produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any cases not sold by the end of the day, they are sold to a large food processing company for $3 per case. The probability that daily demand will be 100 cases is 0.3, 200 cases is 0.4, and 300 cases is 0.3. Farm Grown has a policy of always satisfying customer demand. If it runs out of supply it purchases what’s necessary from a competitor at $16 per case. How many cases do you recommend they produce each day?

## Lab Notes

- TBD