Final answer:
Stratified sampling is the most suitable method for a polling agency to obtain a representative sample of the population when investigating voter support for a ballot measure.
Step-by-step explanation:
The most likely method to provide a representative sample of the population for a polling agency investigating voter support for a ballot measure is B. Stratified sampling. This method involves dividing the population into subgroups (strata) that share similar characteristics and then taking a random sample from each stratum to ensure that the sample reflects the overall population's diversity. This is in contrast to methods like convenience sampling, which can introduce bias and are not likely to be representative because they are based on accessibility rather than randomness.
Other methods referenced, like cluster and quota sampling, may be more cost-effective but may introduce biases or not be as representative of the population as stratified sampling. Snowball sampling is typically used in exploratory qualitative research, where participants recruit other participants, and is not appropriate for obtaining a representative sample for polling purposes.