Question 9
A number in $[0,1]$ is chosen using a fair coin. If the first toss is heads, toss again and choose $0$ for heads or $1$ for tails. If the first toss is tails, choose a real number uniformly from $[0,1]$.
Two numbers $x,y$ are chosen independently by this procedure. What is the probability that $|x-y|\gt \dfrac12$?
Two numbers $x,y$ are chosen independently by this procedure. What is the probability that $|x-y|\gt \dfrac12$?