According to the American Pet Products Association, $68 \%$ of American households own a pet. What is the probability that a randomly selected household does not own a pet?

Step 1 ：According to the American Pet Products Association, 68% of American households own a pet. We are asked to find the probability that a randomly selected household does not own a pet.

Step 2 ：The probability that a randomly selected household does not own a pet is simply the complement of the probability that a household does own a pet.

Step 3 ：Since we know that 68% of households own a pet, we can subtract this from 100% to find the probability that a household does not own a pet.

Step 4 ：Let's denote the percentage of households that own a pet as \(pet_owners = 68\)

Step 5 ：Then the percentage of households that do not own a pet is \(non_pet_owners = 100 - pet_owners = 32\)

Step 6 ：Final Answer: The probability that a randomly selected household does not own a pet is \(\boxed{32\%}\)