So my previous post asked some questions. I want to give the billions of people who read this blog a few days to provide answers rather than just give them away, but I feel it is unfair to simply wait for days when the only (possibly) interesting part of that post was the questions. Therefore, I’ll provide an answer to the first question (deliberately ranked first to enable this) already.
“1) Imagine that you or a computer could pick a number at random from the interval [0,1]. What is the probability that this number will turn out to be a rational number?”
There are infinitely many rational numbers in this interval. The probability that a randomly picked number within this interval will be rational is 0.