Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 2 / 12F / d / Solution

Divide the keystrokes into disjoint blocks of five, and let $A_n$ be the event that block $n$ is exactly HELLO. The events are independent events, andConsequentlyPart (c) shows that infinitely many of these block events occur almost surely. Each occurrence is an occurrence of HELLO in the full typed sequence, so