Final answer:
A probability sample is a sampling method where each member of the population has a known, nonzero chance of being selected. It relies on random sampling techniques to ensure representativeness and to avoid bias. Sampling with replacement allows for multiple selections of the same individual, while without replacement does not.
Step-by-step explanation:
A probability sample is a sample in which each member of the population has a known, nonzero chance of being selected. This type of sampling ensures that every individual in the population has an equal opportunity to be included in the sample, which is crucial for obtaining representative data of the entire population. Random sampling methods such as simple random sampling, stratified sampling, cluster sampling, and systematic sampling are commonly used to achieve a probability sample.
In contrast, nonrandom methods like convenience sampling, which do not give each individual in the population an equal chance of being selected, can result in biased data. It is important to note that in sampling with replacement, individuals can be chosen more than once since they are replaced in the population pool after selection, maintaining the independence of each selection. However, in sampling without replacement, once an individual is chosen, they cannot be picked again, leading to dependent events and a changing probability with each selection.