d) roughly every 30,000 miles. That's
roughly once in 11 years.
There have been two surveys of members of the League of
American Bicyclists (formerly the League of American Wheelmen).
The survey by Kaplan[i]
in 1975 indicated that these riders falls
off their bikes about every 8,500 miles. However, Moritz's survey in 1994[ii]
showed that falls or crashes that actually damage something (more than $50 worth
of property damage, or that need medical treatment) average only about once
every 11 years, or about once every 32,000 miles.
If a "serious" crash every 11 years sounds somewhat scary, please realize that $50 damage (the threshold for the Moritz study) can occur if you merely bend your derailleur or tear your good cycling jacket. The median property damage in these "serious" crashes was only $100; the median medical expense in these "serious" crashes was only $155.
On one hand, it's too bad the study didn't look at truly serious crashes instead - those with lasting consequences. But on the other hand, it's clear that truly serious crashes must be even more rare.