Overall risk from individual risks

[eek2010]

Hi there:

Here's the scenario. A building site has 12 buildings. The risk of fire in each building has been calculated and in some cases is the same, in others different. For example, building one: 1 in 100, building two: one in 1000, building three: 1 in 500...and so on. Is there a calculation to estimate the risk of a fire happening anywhere on the buidling site in any of the buidlings? Have tried adding the different probabilities and dividing the total by the number of buildings but that doesn't seem right? Heeeelp!
Thanks in advance. :?

 

[tkhunny]

This is a very tedious problem unless you make one observation: P(any fire in any building) = 1 - P(no fire an any building)

P(and fire in any building) = 1 - (1 - 1/100)*(1 - 1/1000)*(1 - 1/500)*etc.

REALLY BIG CAVEAT!! This assumes fires are independent. We all know that adjacent buildings are NOT safe when their neighbors catch fire. The assumption of independence is quite dubious in this example.