Can somebody help me with the following probability question? There is none like it to refer to in my textbook and I am confused.

Explain how you would determine the probability that a given household in your community is watching the 10:00m tv news on a Wednesday night?

You are talking about a given (particular) household.

Call them on the phone during the broadcast. The probability is either 1 or zero.

For the probability of a random househod, consult the previous week's Nielsen ratings for your community.