For the following mathematical risk assessment assignment I have a question.

Assume that you need to make a decision on taking safety measures with
respect to a fire in a hotel due to an ashtray causing the fire in one
of the rooms. The probability of an ashtray- fire in a hotel room is
10%. You have the following information about the safety measures and
their reliability (probability of failure) and the related
costs/consequences. The measures are ordered with respect to
prevention of highest to lowest consequences.

Early Detection:

Smoke Dectector:

Sprinkler Room:

Sprinkler Hallway:

• pf: 0.1
• D: 1000000
• I: 50000

make an event tree, and based on the tree, decide whether you would
recommend to make the safety investment (take ALL safety measures) or
not

My attempt:

To be able to draw an event tree, you need to put the event in order first. I decided the following order:

Fire -> Early dection -> Smoke detection -> Sprinkler room -> Sprinkler hallway.

Since each ‘level’ does have 2 options, I can calculate that there are $2^5 = 32$ possible outcomes. But using the context, we know that once a fire prevention system has worked, the the other ‘levels’ have become irrelevant.

But from here on, I am lost. Could I get feedback on this to calculate wheter it is better to have prevention measures or not.

Although, it is not stated in the question. I’m quite curious wheter it could be calculated from this question if there is on number of safety levels that represent the optimal solution? So a solution between all the safety measure and all the safety measures.

It would be extremely helpful if I could get feedback on this.

Thanks in advance