333.Three Heads or Three Tails
★★★markov chainsCh. 6 — Random Variables and Expectation444+ Problems in Probability
Anna and Brenda repeatedly toss a fair coin. Anna wins if 3 heads appear in a row; Brenda wins if 3 tails appear in a row. What is the expected number of tosses until someone wins?
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By symmetry, track only the length of the current run (1 or 2). Two equations, two unknowns.
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