The correct answer is: (A) is true and (R) as per the sampling theory is also fully true.
The law of inertia of large numbers states that, as the number of trials in an experiment increases, the results of the experiment will tend to get closer and closer to the expected value. This law is the basis for sampling theory, which is the study of how to draw a sample from a population in such a way that the sample is representative of the population.
When a reasonably large sized sample is drawn randomly from a given population, it is likely to contain almost all the characteristics of the population. This is because, as the sample size increases, the results of the sample will tend to get closer and closer to the expected value.
The law of inertia of large numbers is a fundamental principle of statistics, and it is used in a wide variety of applications. For example, it is used to calculate confidence intervals and to test hypotheses.
The following are brief explanations of each option:
(A) is true and (R) as per the sampling theory is also fully true. This is the correct answer, as explained above.
(A) is true, but the (R) as per the sampling theory is not fully true. This is not the correct answer, as the law of inertia of large numbers is a fundamental principle of sampling theory.
Both (A) and (R) are false. This is not the correct answer, as (A) is true.
(A) is false, but the (R) is sufficient as per the sampling theory. This is not the correct answer, as (A) is true and (R) is a fundamental principle of sampling theory.