If Mary and John own or use the car together, your example (a) is appropriate
to use in a sentence like this:
Mary and John抯 new car was stolen from their driveway
Conversely, if Mary has one car, and John another, you could use your
example (b) in the sentence
Both Mary抯 and John抯 cars are in the shop.
Or, you could say more comfortably, referring to their two separate
Mary抯 car and John抯 car are both
in the shop.
In joint or group possession, add the possessive marker only to the
last noun of the unit, as in the following example. The concept of 搖nit?
is important here:
Hilary Rodham Clinton and Bill Clinton抯
daughter Chelsea graduated from Stanford University.
In individual possession, add 枓s to each
Hilary Rodham Clinton抯 and Bill Clinton抯
different lives now keep them apart in different cities.