What type of sample ensures that each element has the same probability of being selected?

A simple random sample is a sampling method where every individual or element in the population has an equal chance of being selected. This is achieved through randomization techniques, such as using random number generators or drawing names from a hat, ensuring that the selection process does not favor any particular group or characteristic within the population. Because of this equal probability, simple random sampling reduces the likelihood of bias and provides a representative snapshot of the population.

In contrast, convenience sampling selects individuals based on ease of access, which does not guarantee that every member of the population has a chance of being included, thus potentially introducing bias. Stratified sampling involves dividing the population into homogeneous subgroups (strata) and then sampling from each group, which is useful for ensuring representation of each subgroup but does not give every individual an equal chance overall. Cluster sampling, similar to stratified sampling, involves dividing the population into clusters and then randomly selecting entire clusters, which does not ensure equal probability for each individual in the population as some individuals could be excluded depending on cluster selection.

Therefore, the key characteristic that distinguishes a simple random sample is the equal probability of selection for all individuals, making it a fundamental method in statistical sampling.