From an insurance perspective how many auto accidents invovle only one
third party claim? That is, if car 1 hits car 2, what are the odds
that there is only one person is in car 2?

I'm not sure that this is a question which can be given a definite
answer.  I can tell you that after working as an auto claims adjuster
for two major national insurance companies over the last several
years, the vast majority of claims I deal with involve only one person
in each involved vehicle.  I would say it is on the order of 70-80%.

When there are passengers in the vehicle, they tend to be minors (ie,
parents transporting their children).

I hope that is of some use to you.