284.First to Two Heads
★★★markov chainsCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
Alice and Bob alternate tossing a fair coin, Alice first. The first person to accumulate two heads in total (not necessarily consecutive) wins. What is the probability that Alice wins?
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First-step analysis on states (Alice's heads, Bob's heads) at the start of Alice's turn. Solve from the endgame states backwards.
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