A probability sampling is a method of investigation that uses a random sample. This type of random sampling ensures that all different categories in your study have the same probability of being chosen.

For example, a study that might use a probability sample is an investigation of voters' views about an election because the investigator will want to get a wide range of views and make sure that he or she is getting a random sample. Studies can use simple random sampling and assign all voters to what's called the sampling frame (the complete list of total subjects) and then have a computer pick out certain voters for interviewing. Another way to approach this study is to use stratified random sampling. In this method, the population is divided into certain categories, such as voters from ages 18-30, 31-50, 50-80, over 80, etc. The study would try to get the same number of people in each category to make sure the investigator is studying different sub-groups in the population and that the investigator can make subgroup comparisons. The study can also use cluster random sampling. In this method, the population is divided into clusters, usually by geographic region, and then the investigator chooses certain clusters or areas with the sample randomly. Within the chosen clusters (which might be counties), each town is sampled. For example, the study might look at voters within Massachusetts. Each county would be a cluster, and a few counties would be chosen. Within each county, voters in each town would be sampled. These are different methods of random sampling with a probability sample. 

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.