First HH on the tenth toss

A fair coin is tossed until two heads appear in a row ( $HH$ ). What is the probability that this first happens on exactly the $10$ th toss?

Show hints (2)+

Stop at toss $n$ : tosses $n-1,n$ are $HH$ , no earlier $HH$ . Valid sequences number $F_{n-1}$ .
$\mathbb{P}=F_{n-1}/2^n$ ; with $F_9=34$ , that's $34/1024$ .

Answer

Reveal answer →

0.0332 (± 0.0005)

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