Combining related probabilities I understand that to calculate the probability of two independent events both happening, one can simply multiply the probabilities.
However, consider the following:
A list of counties in the East coastal U.S. Each county has a calculated probability of a hurricane making landfall next year. I am trying to calculate the probability of a hurricane making landfall across multiple counties at the same time, i.e. three counties being effected in a single year. However, many counties are either in the same state, or in adjacent states, so they are not “independent”.
For example (county, probability)
Cameron .045
Hidalgo .049
Willacy .023
Kenedy  .064

For these counties, as a single hurricane may affect multiple counties, how should one think about calculating a combined probability of these four counties experiencing a landfall hurricane next year?
Further, any thoughts on how to apply a decreasingly related probability towards independence?  (two counties very far from each other, opposite ends of the eastern US, for example).
 A: Let's consider a simpler 1-D situation as in below image. 

Each square represents a county. Aim is to compute probability that it rains in C and in R6. Let $$Pr(raining\space in\space C) = Pr(C)$$ $$Pr(raining\space in \space R1) = Pr(R1) $$ and so on.
Joint probability $$Pr(C , R6) = Pr(R6) \cdot  Pr(C|R6)$$
We know $$P(R6)$$ but to compute $$P(C|R6)$$ we proceed from right to left.
$$Pr(R5|R6) = \dfrac{Pr(R4) \cdot Pr(R6) + (1-Pr(R4)) \cdot Pr(R6)}{2}$$
Further,
$Pr(R4|R6) = \dfrac{Pr(R3) \cdot Pr(R5|R6) + (1-Pr(R3)) \cdot Pr(R5) + Pr(R3) \cdot (1-Pr(R5|R6)) + (1-Pr(R3)) \cdot (1-Pr(R5|R6))}{4}$    
$Pr(R3|R6) = \dfrac{Pr(R2) \cdot Pr(R4|R6) + (1-Pr(R2)) \cdot Pr(R4|R6) + Pr(R2) \cdot (1-Pr(R4|R6)) + (1-Pr(R2)) \cdot (1-Pr(R4|R6))}{4}$
...
$Pr(C|R6) = \dfrac{Pr(L1) \cdot Pr(R1|R6) + (1-Pr(L1)) \cdot Pr(R1|R6) + Pr(R2) 
\cdot (1-Pr(R1|R6)) + (1-Pr(L1)) \cdot (1-Pr(R1|R6))}{4}$
Here, assumption is that rain in L1 is not affected by rain in R6 (Any suggestions for a better formulation are welcome).
If we have a 2-D case, perhaps a similar line of argument might be applied. But it seems much more complicated.
A: There are many ways to approach this - I identified three very different questions that would significantly change your approach. All of these approaches would require some of the underlying data the risk projections are based on, and not just the published statistics for each county.
Can you provide some more information about the type of question you want to answer? Also, do you have access to or are you willing to compile historical data on hurricane risk by county?
Any specific combination of counties
Could be helpful for general portfolio risk analysis for real estate owners, insurers
General Model of Hurricane risk relations (a lot of effort for a good one, maybe not too much effort for a basic one)
Historical-data-driven correlation matrix (likely too sparse)
One, or small number of specific combinations of counties
Could be helpful for a specific property owner or insurer localized to one region
Individualized analysis (best able to account for locally varying factors like county size and geography)
How many counties are impacted in a year / in a hurricane
Could be helpful for government agencies trying to build cross-county communications for coordinating emergency management
Historical data (Very easy!)
