Even-size, non-empty subset

A subset of {1,,10}\{1,\dots,10\} is chosen by including each element independently with probability 1/21/2. What is the probability the subset has even size and is non-empty? (to 3 decimals)

Show hints (2)+
  1. Even-size subsets number 2^9 = 512 (half of all subsets).
  2. The empty set is even-sized - subtract it before dividing by 2^10.

Answer

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0.499 (± 0.001)

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Asked at: EV & Betting Games, Data-Driven Research

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