Step 1 :The probability distribution of the number of televisions per household in a small town is given as follows: \(P(0) = 0.02\), \(P(1) = 0.16\), \(P(2) = 0.25\), and \(P(3) = 0.57\).
Step 2 :For part (a), we need to find the probability of randomly selecting a household that has two or more televisions. This can be found by adding the probabilities for 2 and 3 televisions: \(P(2) + P(3) = 0.25 + 0.57 = 0.82\).
Step 3 :For part (b), we need to find the probability of randomly selecting a household that has between one and three televisions, inclusive. This can be found by adding the probabilities for 1, 2, and 3 televisions: \(P(1) + P(2) + P(3) = 0.16 + 0.25 + 0.57 = 0.98\).
Step 4 :For part (c), we need to find the probability of randomly selecting a household that has at most two televisions. This can be found by adding the probabilities for 0, 1, and 2 televisions: \(P(0) + P(1) + P(2) = 0.02 + 0.16 + 0.25 = 0.43\).
Step 5 :Final Answer: (a) The probability of randomly selecting a household that has two or more televisions is \(\boxed{0.82}\). (b) The probability of randomly selecting a household that has between one and three televisions, inclusive, is \(\boxed{0.98}\). (c) The probability of randomly selecting a household that has at most two televisions is \(\boxed{0.43}\).