What are the odds of any one library being affected by a major
disaster during its existence? (a major disaster affects at least 10%
of the holdings)

Someone versed in insurance for governmental institutions would likely
know the answer. I certainly don't, but would be interested in the
answer. I think $5 is too low a price for such a question.

I have worked in libraries, though.

Libraries tend to be very strong and remarkably well-sprinklered and
well-smoke-detectered fireproof buildings, engineered to take whatever
Mother Nature in its location might be expected to deliver them,
making them resistant to most destructive forces (earthquakes, floods,
hurricaines, tornados, and the such).

The real risk is fire, and the damage the sprinklers do to the
collection. For a valuable collection, the sprinkler system would be
zoned (i.e., the whole building would not be flooded, only the area
where heat or smoke indicated there was a problem). Books, on the
whole, are not that valuable, and few are difficult to replace.

Extremely valuable collections would be stored in considerably safer
conditions. A Gutenberg Bible or a first edition double elephant folio
of Audoban's <i>Birds of America</i> are given the protection worthy
of national treasures.

Short of an act of war, I believe the odds that a genuinely valuable
collection would suffer some loss is quite low, a very small fraction
of one percent per year. For the regular public or college library,
the odds are probably nearly as low.

I speak only of American libraries.

As asked, the question seems very hypothetical since there are
libraries and LIBRARIES, such as the one in in Weimar, Germany, that
recently suffered from a terrible fire and the water damage Waukon
mentions.  And that library was a major depository for German
literature, known for the value of its collection and and the
historical importance of its building  - but still absolutely deficit
in fire protection.
The majority of libraries have little that is of unique value, so a
question about "the odds of any one library ..." is fairly
unimportant.

I know there was a Library in New Zealand where a person put a hose
through the Book Return and turned it on. I think it was over a
weekend, certainly several days. Lots of damage. Naughty person was
found and went to court. Can't remember the sentence (maybe a whole
BOOK of them would have been appropriate!)