Refined taste

Classical Mechanics Level 5

You are organizing a surprise concert for Jamie xx, to hype his new album, 'In Colour'. You want to fill the space with a large concentration of his fans, although they aren't too common in the general population. In service of your quest, you rent out two art galleries, separated by a few city blocks. In both of the galleries, you play old Jamie xx songs.

People are free to enter the first gallery from the street, and don't know what it is all about when they decide to go in. There is also a shuttle that takes everyone from the first gallery to the second, once an hour. Moreover, the only way to get into the second gallery is by taking the shuttle.

Importantly, people can leave either gallery through an exit door, and there is an asymmetry between Jamie xx fans and non-Jamie xx fans in exiting the galleries. Fans of Jamie xx spend an average of 2 minutes in the gallery before leaving, while people who don't like Jamie xx's music will leave in 10 seconds.

After a long time has passed, what fraction of people in the second gallery are fans of Jamie xx?

Assumptions and Details

  • Neither gallery gets near its maximum capacity.
  • Only 1% of people in the general population are Jamie xx fans.

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