Here is what I read from this problem:

Conditions a) and b) suggest that 15% insure EXACTLY one car.

A = exactly one car

P(A) = 0.15

P(A_) = 0.85

B = insure a sports car

P(B) = 0.23

P(B_) = 0.77

68% insure more than one car BUT no sports car --> P(A_ and B_) = 0.68

Want: P(A and B_) = P(A|B_)P(A) = P(B_ |A) P(B_)

still thinking.