Step 1: Understanding probability sampling.
Probability sampling refers to a sampling method in which each member of the population has an equal chance of being selected. It includes methods such as simple random sampling, stratified sampling, and systematic sampling.
Step 2: Analyzing the options.
- (A) Incorrect, standing in front of the library and handing out questionnaires is a form of convenience sampling, not probability sampling.
- (B) Incorrect, sending the questionnaire through email does not involve random selection, which is necessary for probability sampling.
- (C) Correct, selecting students through a lottery from a roster provided by the administration is a form of random selection, which fits the definition of probability sampling.
- (D) Incorrect, giving the questionnaires to a data collection agency does not ensure a probability sampling method unless the agency uses a probability sampling technique.
Step 3: Conclusion.
Thus, the correct answer is (C) Collect the roster of students from the college administration and give the questionnaire to those selected through a lottery.