2024 SSMO Accuracy Round Problems/Problem 10

Problem

Bobby is spinning a rigged wheel with three sections labeled $A,B,$ and $C.$ Two integers $0\leq x,y\leq 50$ are chosen randomly and independently, such that there is a $x\%$ chance the wheel lands on $A$ and a $y\%$ chance the wheel lands on $B.$ Given that the wheel lands on $C$ the first time, the probability that it will land on $C$ if Bobby spins it again can be expressed as $\frac{m}{n},$ for relatively prime positive integers $m$ and $n.$ Find $m+n.$

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2024 SSMO Accuracy Round Problems/Problem 10

Problem

Solution