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MathNet 2016-part-07 — 182 problems (EN–VI) Question 97

Math Olympiad Vault · MathNet 2016-part-07 — 182 problems (EN–VI)

Question 97

Michael is playing basketball. He makes $10\%$ of his shots, and gets the ball back after $90\%$ of his missed shots. If he does not get the ball back he stops playing. What is the probability that Michael eventually makes a shot?

Proposed by: Eshaan Nichani