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MathNet 2022-part-04 — 197 problems (EN–VI) Question 58

Math Olympiad Vault · MathNet 2022-part-04 — 197 problems (EN–VI)

Question 58

Bryce plays a game in which he flips a fair coin repeatedly. In each flip, he obtains two tokens if the coin lands on heads, and loses one token if the coin lands on tails. At the start, Bryce has nine tokens. If after nine flips, he also ends up with nine tokens, what is the probability that Bryce always had at least nine tokens?

(a) $1/7$
(b) $1/6$
(c) $5/28$
(d) $17/84$