In the unrestricted probability sampling design, more commonly known as simple random sampling every element in the population has a know and equal chance of being selected as a subject. Let us say there are 1000 elements in the population and we need a sample of 100. Suppose we were to drop pieces of paper in a hat, each bearing the name of one of the elements, and draw 100 or those from the hat with our eyes closed. We know that the first piece drawn will have a chance of being drawn; the next one is a chance of being drawn and so on.

In other words we know that the probability of any one of them being chosen is 1 in the number of the population and we also know that each single element in the hat has the same or equal probability of being chosen. We certainly know that computers can generate random numbers and one does not have to go through the tedious process of pulling out names from a hat.

When we thus draw the elements from the population, it is most likely that the distribution patterns of the characteristics we are interested in investigating in the population are also likewise distributed in the subjects we draw for our samples.

SIMPLE RANDOM SAMPLING: In this type of sampling, the chance of any one element of the parent pop being included in the sample is the same as for any other element. By extension, it follows that, in simple random sampling, the chance of any one sample appearing is the same as for any other. There exists quite a lot of misconception regarding the concept of random sampling: Many a time, haphazard selection is considered to be equivalent to simple random sampling. For example, a market research interviewer may select women shoppers to find their attitude to brand X of a product by stopping one and then another as they pass along a busy shopping area --- and he may think that he has accomplished simple random sampling! Actually, there is a strong possibility of bias as the interviewer may tend to ask his questions of young attractive women rather than older housewives, or he may stop women who have packets of brand X prominently on show in their shopping bags!. In this example, there is no suggestion of INTENTIONAL bias! From experience, it is known that the human being is a poor random selector --- one who is very subject to bias. Fundamental psychological traits prevent complete objectivity, and no amount of training or conscious effort can eradicate them. As stated earlier, random sampling is that in which population units are selected by the lottery method.

Since it is generally impossible to study an entire population (every individual in a country, all college students, every geographic area, etc.), researchers typically rely on sampling to acquire a section of the population to perform an experiment or observational study. It is important that the group selected be representative of the population, and not biased in a systematic manner. For example, a group comprised of the wealthiest individuals in a given area probably would not accurately reflect the opinions of the entire population in that area. For this reason, randomization is typically employed to achieve an unbiased sample. The most common sampling designs are simple random sampling, stratified random sampling, and multistage random sampling

Statistics is the numerical statement of facts capable of analysis and interpretation. Science of statistics is the study of statistical principles and methods applied in collecting, presenting, analysis and interpretating the numerical data in any field of inquiry. Science of facts and figures is called statistics.

The sampling in which samples are selected at random is called simple random sampling. A simple random sample is selected in such a way that each possible sample of a given size has the same probability of selection.