Equal Probability and Nonzero Probability

Equal Probability:

The term equal probability is frequently used in the theory of sampling. This term is quite often not understood correctly. It is thought to be close to ‘equal’ in meaning. It is not true always. Suppose there is a population of 50(N = 50) students in a class. We select any one student. Every student has probability 1/50 of being selected. Then a second student is selected. Now, there are 49 students in the population and every student has 1/49 probability of being selected. When the first student is selected, all the students have equal (1/50) chance of selection and when the second student is selected, again all the students have equal (1/49) chance of selection. But 1/50 is not equal to 1/49. Thus equal probability of selection means the probability when the individual is selected from the remaining available units in the population. At the time of selecting a unit, the probability of selection is equal. It is called equal probability of selection.

Known Probability:

In sampling theory the term known probability is used in random (probability) sampling. Let us explain it by taking an example. Suppose there are 300 workers in a certain factory out of which 200 are skilled and 100 are non-skilled. We have to select one sample (sub-sample) out of skilled workers and one sample out of un-skilled workers. When the first worker out of skilled workers is selected, each worker has a probability of selection equal to 1/200. Similarly when the first worker out of un-skilled workers is selected, each worker has a probability of selection equal to 1/100. Both these probabilities are known,though they are not equal.

Non-Zero Probability:

Suppose we have a population of 500 students out of which 50 are non-intelligent. We have decided to select an intelligent student from the population. The probability of selecting an intelligent student is 1/450 which is non-zero. In this example, we have decided to exclude the non-intelligent students from the population for the purpose of selecting a sample. Thus probability of selecting a non-intelligent student is zero.