Re: [math-fun] Should I be surprised?

James Propp <jamespropp@gmail.com> wrote:

The 91st Fibonacci number is 4,660,046,610,375,530,309

Should I be surprised that the first eight digits are even?

Should I be surprised that, if you strip out the zero-digits, this number consists of six even digits followed by eight odd digits?

No. This is called the Texas Sharpshooter Fallacy. The a priori odds of that exact pattern are small, but it's taken from vast population of equally unlikely patterns, e.g. that in base 17 the digits of the 23rd Catalan number are in ascending sequence if you exclude the digit "3." (I just made that up; I haven't checked. If by remarkable coincidence that actually *is* true, that's *not* an example of the fallacy, since I "claimed" it before checking.)