Overlap of two random intervals in the unit line

Draw four independent $\text{Unif}(0,1)$ values $X_1,\dots,X_4$. Form one interval with endpoints $X_1,X_2$ and another with endpoints $X_3,X_4$. What is the probability that the two intervals intersect?

$2/3$. Look at the smallest of the four points. Its partner is equally likely to be the 2nd, 3rd or 4th smallest. The intervals are disjoint only if it is the 2nd smallest, so they overlap with probability $\tfrac23$.