 The fourth section continues the trend of practical applications by discussing applications of probability to <unk> , <unk> , and <unk> , or to personal , judicial , and financial decisions . In this section , Bernoulli differs from the school of thought known as <unk> , which defined probability in an empirical sense . As a counter , he produces a result resembling the law of large numbers , which he describes as predicting that the results of observation would approach theoretical probability as more trials were held — in contrast , frequents defined probability in terms of the former . Bernoulli was very proud of this result , referring to it as his " golden theorem " , and remarked that it was " a problem in which I ’ ve engaged myself for twenty years " . This early version of the law is known today as either Bernoulli 's theorem or the weak law of large numbers , as it is less rigorous and general than the modern version . 
