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Yunsoo has ten cups face down and one cup has a $100 bill under it. You...

Yunsoo has ten cups face down and one cup has a $100 bill under it. You select cup 1. Yunsoo then groups cups 2-4 together into group A and cups 5-10 together into group B. He then flips all but one cup over in both groups to reveal that they do not have the $100 bill. What are your probabilities of winning for each of the remaining cups? Which cup should you choose to have the highest chance of winning?

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