Answer:
28.75% probability that none of the three randomly selected households own a cat
Explanation:
For each household, there are only two possible outcomes. Either it owns a cat, or it does not. The probability of a household owning a cat is independent of other households. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
34% owned a cat
This means that

Three households are selected
This means that

What is the probability that none of the three randomly selected households own a cat?
This is P(X = 0).


28.75% probability that none of the three randomly selected households own a cat