Finite Geometric Series — Practice problem

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Contributors

Expii Solve
Alex Federspiel
Sarah Walker

\text{La La Landing a Role}

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At the 89th Academy Awards La La Land won $6$ Oscars, after achieving $14$ nominations. La La Land tells the story of two aspiring entertainers in a world filled with talent vying for opportunity. Each year, millions of people dream of being movie stars, but only a few ultimately make it into the role.

Suppose that your chance of being cast for a certain role is proportional to your skill level. If you are $1$ of $100$ people auditioning, and everyone is equal in skill level, then your chance of being the one cast is $1$ %. Now let's suppose that your skill level is the highest among the $100$ people, and it's twice that of the next person, whose skill is twice that of the next person, whose skill is twice that of the next person, and so on, all the way to the $99$ th person, whose skill is twice that of the last person, about what is your chance of being cast?