MathDB

Marisa has a collection of

2^8-1=255

distinct nonempty subsets of

\{1, 2, 3, 4, 5, 6, 7, 8\}

. For each step she takes two subsets chosen uniformly at random from the collection, and replaces them with either their union or their intersection, chosen randomly with equal probability. (The collection is allowed to contain repeated sets.) She repeats this process

2^8-2=254

times until there is only one set left in the collection. What is the expected size of this set?

Problem Statement