Step 1 :The probability distribution of the number of televisions per household in a small town is given as follows: \[\begin{array}{lcccc} \mathbf{x} & 0 & 1 & 2 & 3 \\ \mathbf{P}(\mathbf{x}) & 0.02 & 0.16 & 0.25 & 0.57 \end{array}\]
Step 2 :We are asked to find the probability of randomly selecting a household that has one or two televisions.
Step 3 :To do this, we need to add the probabilities of selecting a household with one television and the probability of selecting a household with two televisions.
Step 4 :The probability of selecting a household with one television is 0.16 and the probability of selecting a household with two televisions is 0.25.
Step 5 :Adding these two probabilities together gives us a total probability of 0.41.
Step 6 :Final Answer: The probability of randomly selecting a household that has one or two televisions is \(\boxed{0.41}\).