Anon10/17/25, 22:36No.16819635
Call their arrival times tR and tJ. Let's say we choose a tR value. If it's not near the boundaries (8am, 9am), there is a 30min window surrounding tR where tJ will lead to a meeting i.e. a 50% chance (30mins/60mins). If tR is chosen within 15 mins of the boundaries, the effective window for tJ goes down linearly to 50% of its "normal" value. This effectively multiplies the contribution of those tR values by 0.75 since we are integrating a triangle+rectangle of equal heights instead of a rectangle. This applies to exactly half of the tR values. So the probability is
0.5 * 0.5 (from "middle" values not near boundaries)
+ 0.75 * 0.5 * 0.5 (from values near the boundary)
= 7/16