What two important probability principles were established in this exercise?

In this exercise, two important probability principles established are the Law of Large Numbers and the Central Limit Theorem. The Law of Large Numbers states that as a sample size increases, the sample mean will converge to the expected value of the population. Meanwhile, the Central Limit Theorem asserts that the distribution of the sample means will approach a normal distribution, regardless of the original population's distribution, as the sample size becomes sufficiently large.