Recently, Taylor Shobe posted a problem
which is based on Marilyn vos Savant's Sunday Column on this subject
The question seems straightfoward, which shall be phrased as follows
A die is thrown 20 times, and a report is made of the recorded outcomes. Which is more likely to be the report, A or B?
The phrasing of this problem turns out to be critical. As originally phrased, Taylor's problem raised objections by a number of people, including Calvin Lin, but as it stands now, it should almost be correctly worded for the answer of "B is more likely*, which is the common sense answer. Of course a die thrown randomly 20 times is going to generate a result like B, and nobody would be expecting A. And yet, how is it mathematically decided that B is more likely than A? If the question had been
Which sequence A or B is the more likely outcome?
then the correct answer would be "equally likely", since the probability of either happening is in
Can anyone throw some light on this subject? If the "common sense answer" is "B is more likely", how is that decided mathematically? Making the argument that "there's a lot more random sequences of digits than there are sequences where all the digits are the same" is not sufficient, since it involves opinions about what is random and what is order. For instance, given C and D
why are we likely to say that D is more likely than C? We can claim that C is "more ordered", but try quantifying that mathematically.