Color switches in a draw

An urn has 20 balls, 8 red and 12 blue. You draw 5 without replacement and lay them out in the order drawn. What is the expected number of color changes — positions where a ball's color differs from the one immediately before it (so among the 4 adjacent pairs)? Give a decimal to four places.

Show hints (2)+
  1. Put an indicator on each of the 4 adjacent pairs; sum by linearity.
  2. One adjacent pair is bichromatic with probability 282012192\cdot\tfrac{8}{20}\cdot\tfrac{12}{19}.

Answer

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2.0211 (± 0.001)

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Asked at: Citadel, IMC

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