Position of the first spade

Cards are turned over one at a time from a shuffled deck. What is the expected position of the first spade? Give a decimal to four places.

Show hints (2)+
  1. Use the gaps formula for kk successes among nn.
  2. E=n+1k+1E=\tfrac{n+1}{k+1} with n=52,k=13n=52,k=13.

Answer

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3.7857 (± 0.001)

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