The Leaf Audit

A chance tree is audited in one sweep: multiply along every path, add across the leaves, and confirm the total is exactly 1.

The ferry trip, drawn whole. Two branchings: on time 0.9 or late 0.1, then ferry running 0.8 or not 0.2. Four leaves, multiplied along their paths: on-time-and-running, 0.72; on-time-and-boat-down, 0.9 × 0.2 — 0.18; late-but-running, 0.1 × 0.8 — 0.08; late-and-down, 0.02. Now add across: 0.72 plus 0.18 plus 0.08 plus 0.02 — exactly 1.00. The books balance, so no case was lost or invented, and any question about the trip is now a matter of picking leaves: the chance of catching the boat at all is the first leaf alone, 0.72; the chance of a wasted ride is the second, 0.18.