Let Z be the number of the first toss in which we see a tail coming after a head.
What is the Expected value of Z (Mean)?
I figured out that for the Z-1 times the is the geometric for the first head appear.
2026-03-29 12:40:32.1774788032
Flip the coin until a tail coming after the head
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Denote the desired expected value by $x$. If you get heads first, you then have to wait for tails with success probability $p=\frac12$ and thus expected time $1\div\frac12=2$. If you get tails first, you're back to where you started. Thus
$$ x=1+\frac12(2+x) $$
Solving for $x$ yields $x=4$.