Suppose a number, $x$, is picked randomly from the interval $[0,1]$. What is the probability that $x=1/10$? What is the probability that $x=m/10$ for some $m=0,....,10$. What is the probability that $x=m/100$ for some $m=0,...,100$? What is the probability that $x=m/n$ for some $m \le n$? What is the probability that x is rational?
Not sure how to do this. I know with an increasing sequence, the probabilities of $P(A_n)$ grow with $n$ and approach the union and with a decreasing sequence the probabilities of $P(A_n)$ get smaller with $n$ and approach the intersection. How is this useful in the given problem?