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HMMT November 2016 U10

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Michael is playing basketball. He makes 10%10 \% of his shots, and gets the ball back after 90%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?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{10}{19}

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