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, however that is not always true. Suppose there is a population of 50(N = 50) students in a class and we select any one student. Every student has a 1/50 probability of being selected. Then a second student is selected. Now, there are 49 students in the population and every student has a 1/49 probability of being selected. When the first student is selected, all the students have an equal (1/50) chance of selection and when the second student is selected, again all the students have an equal (1/49) chance of selection. But 1/50 is not equal to 1/49. Thus, equal probability of selection means that when an individual is selected from the remaining available units in the population, at the time of selecting the unit, the probability of selection is equal.

Known Probability

In sampling theory the term known probability is used in random (probability) sampling. Let us explain it with an example. Suppose there are 300 workers in a certain factory, out of which 200 are skilled and 100 are unskilled. We have to select one sample (sub-sample) out of the skilled workers and one sample out of the unskilled workers. When the first worker out of the skilled workers is selected, each worker has a probability of selection equal to 1/200. Similarly when the first worker out of the unskilled 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 unintelligent. 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 unintelligent students from the population for the purpose of selecting a sample. Thus, the probability of selecting an unintelligent student is zero.