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MathNet 2022-part-06 — 196 problems (EN–VI) Question 47

Math Olympiad Vault · MathNet 2022-part-06 — 196 problems (EN–VI)

Question 47

"Very Frustrating Game" has six levels. When a level is attempted, the player goes to the next level if they succeed, but back to the previous level if they fail (or if they are on level 1 they restart).

a) Aerith has a $\frac{1}{2}$ success rate on all levels. How many level attempts on average would it take her to complete the game?

b) Bob has a $\frac{1}{3}$ success rate on all levels. How many level attempts on average would it take him to complete the game?