maximum possible probability 75% of the customers of ACME Mutual Insurance have auto insurance, and 40% have homeowners insurance. What is the maximum possible probability that a randomly selected customer with auto insurance does not have homeowners insurance? i did the approach P(a)-P(A and B) but the answer is .8 i dont know how

Let A be the set that have auto insurance and B the set that have homeowners insurance and U denote universal set. You want to maximize, $$P(B^c|A)$$ $$P(B^c|A)= \frac{P(B^c \cap A)}{P(A)}$$ $$P(B^c|A)= \frac{P(A\setminus A\cap B)}{P(A)}$$ $$P(B^c|A)= \frac{P(A) - P(A\cap B)}{P(A)}$$ $$P(B^c|A) \leq 1-\frac{0.15}{0.75}$$ $$P(B^c|A) \leq 0.8$$