Simple random sampling is a type a unrestricted random sampling in which each, and every item of the universe is selected by chance, without interference of any bias or purpose on the part of the investigator. In such a technique, every item of the universe is given an equal chance of being included in the sample without any restriction, or special condition being imposed for any particular item. However, it may be subjected to a general condition like replacement or non-replacement of the items selected earlier. If an item selected earlier is replaced before making another selection, the technique is called “Simple random sampling with replacement”. If, on the other hand, the item selected earlier, is not allowed to be replaced before making another selection, the technique is called “Simple random sampling without replacement”. A simple random sampling with replacement amounts to sampling from an infinite universe even when it is drawn from a finite universe for that in such case, the total number of units of the universe always remains the same. Thus, simple random sampling is one:
(i) In which the sample items are selected independently of each other, and
(ii) In which all possible samples of a given size have the same probability of being selected.
Thus, if a sample size n is drawn without replacement from a population of size N, then there are possible samples. In such a case, the probability of the sample is given by p = 1/Ncn. If, on the other hand, the sample is drawn with replacement, then there are N possible samples of size n. In such cases, the probability of the sample is given by p =1/Ncn