Suppose you have some location or small area, call it location A, and you have decided for this location the 1-in-100 year event for some magnitude in that area is ‘x’. That is to say, the probability of an event with magnitude exceeding ‘x’ in the next year at location A is 1/100. For clarity, I would rather state the exact definition, rather than say ‘1-in-100 year event’. Now suppose you have a second location, call it location B, and you are worried about an event exceeding ‘x’ in the next year at either location A or location B. For simplicity suppose that ‘x’ is the 1-in-100 year event at location B as well, and suppose also that the magnitude of events at the two locations are probabilistically independent. In this case “an event exceeding ‘x’ in the next year at either A or B” is the logical complement of “no event exceeding ‘x’ in the next year at A, AND no event exceeding ‘x’ in the next year at B”; in logic this is known as De Morgan’s Law. This gives us the result: Pr(a...
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