Write a research problem that would be best studied using a non-probability sample.

Non-probability sampling does not use a random sample, and, therefore, researchers can not assume that the sample represents the population as a whole. Non-probability sampling is often conducted on purpose when it is not feasible or economical to carry out a probability sample (which uses random selection). Sometimes, non-probabilty sampling is done by accident, when researchers, for example, only use college students in their studies (as such subjects are easily available to researchers in universities).
An example of when a researcher might want to use a non-probability sample is the study of what medical experts in the cardiology field think about a procedure such as a new method for heart surgery. This study will not involve large numbers of subjects but instead will choose from the small population of doctors who work in cardiology and will ask these doctors' opinions. Using such a sample is useful in this case because the researcher is not interested in what a wider sample thinks of the procedure, and the researcher knows that the doctors' opinions do not represent a random sample and therefore can not be generalized to larger populations--such as doctors as a whole or to larger populations.