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Omni-MATH / Andrea flips a fair coin repeatedly, continuing until she either flips two heads…

Problem

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problem

Andrea flips a fair coin repeatedly, continuing until she either flips two heads in a row (the sequence HHH H ) or flips tails followed by heads (the sequence THT H ). What is the probability that she will stop after flipping HHH H ?
Plain-text mathematical notation (without MathML)
Andrea flips a fair coin repeatedly, continuing until she either flips two heads in a row (the sequence HH ) or flips tails followed by heads (the sequence TH ). What is the probability that she will stop after flipping HH ?
Original LaTeX notation
Andrea flips a fair coin repeatedly, continuing until she either flips two heads in a row (the sequence $H H$ ) or flips tails followed by heads (the sequence $T H$ ). What is the probability that she will stop after flipping $H H$ ?

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