No, the LLN is a much stronger result than this. It says that you are likely to get close to 17 ONEs in 100 rolls of a die.  This is the fundamental thing that makes statistics worthwhile: if you have a lot of observations then the average of the sample is close to the average of the population. This is why you can , eg, do clinical trials in only a few thousand people and extrapolate to approving drugs for a population of hundreds of millions.   I agree that the article could use revision in the introduction.  I don't really like the proof, either. Only a very small number of people will understand it, and for them there is a simpler, shorter proof under similar assumptions: by algebra the variance of a sum is proportional to the number of summands, and so the variance of an average decreases as the number of summands increases. (TSL)