Solution
= 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>, and
$$
\mathbb P(A_n)=26^{-5}.
$$
Consequently
$$
\sum_{n=1}^{\infty}\mathbb P(A_n)=\infty.
$$
Part (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
$$
\boxed{\mathbb P(\text{HELLO appears infinitely often})=1}.
$$