Problem of the Day #87

POTD March 5, 2024

$3$ points $A,B,C$ are randomly chosen on the circumference of a circle. If $A,B,C$ all lie on a semicircle, then the probability that all of the angles of triangle $ABC$ are less than $120^{\circ}$ can be written as $\frac{m}{n}$, where $m,n$ are relatively prime positive integers. Find $m+n$.