During the summer holidays, there is a street with nine empty houses. There is a burglar committed

to break into one of them during the night. The burglar behaves in a rational manner - he wants to

steal as much as he can, without getting caught and going to jail.

There are three small houses, three medium and three large. In each of them there are jewels worth

100k (small houses), 300k (medium houses) or 1M USD (large houses). The burglar knows this from

his past experience and we can treat this information as a fact. He also knows that 80% of the large

houses, 50% of the medium houses and 25% of the small houses have alarm systems.

In order to get into a house, the burglar needs to bypass a fence and then break in through either a

door or a window. The burglar is aware of the following facts:

Bypassing the fence takes between 5-15 mins and is a uniform distribution

Bypassing a window takes 5-10 mins and is a uniform distribution but there is a 50%

chance that the alarm will trigger

Bypassing a door takes 20-45 mins, is a uniform distribution and alarm will fire only

10% of the time.

In addition, there is a regular security patrol in the neighbourhood. They patrol this particular street

every 2 hours, but if an alarm is triggered, they will respond immediately and the burglar will go to

jail. The burglar only knows the frequency of the patrol, not the specific hour when they will pass.

How would you answer the following questions?

1. What is the probability that 1M USD would be successfully stolen?

2. What is the probability that an attempt would be made on a medium sized house?

Comment:

Some important information is missing. Please use your experience to identify any assumptions

made in order to quantify the uncertainty related to that assumption.