  Take a large bag of black and white beans, with all possible proportions
considered initially equally likely, and imagine to make random extractions
with reintroduction. Twenty consecutive observations of black make us highly
confident that the next bean will be black too. On the contrary, the
observation of 1010 black beans and 990 white ones leads us to judge the two
possible outcomes about equally probable. According to C.S. Peirce this
reasoning violates what he called "rule of balancing reasons", because the
difference of "arguments" in favor and against the outcome of black is 20 in
both cases. Why? (I.e. why does that rule not apply here?)

History and Overview;Probability;Data Analysis, Statistics and Probability